As far as we know IRL, mech fights will not be good way to wage a war, so this answer is meant more as an excuse for the writer, not the actual reasons. That said...

Limited ammo.

Sword would weight about the same as two, three rockets? But with it, you could destroy more than three enemy mechs, if you are good enough pilot.

This does not make sense if you are close to your supply lines and your nation's resources are not limited. But guided missiles can cost millions of USD. Literally. Thousands is pretty normal, if not cheap. Even not guided are expensive. for the cost of few reloads, you could get one more mech. And of course you would need either transport mech to bring rockets to your line, or keep non-mech supply lines. These would be pretty hard to defend. Tanks, using non-rocket missiles, can carry more ammo, but they are low and can withstand a lot of recoil. Mechs, as high bipedals, cannot. So no large ammo storage for them, and no cheap ammo for them.

Even if you can afford to make and deliver enough rockets, it won't work for special units you would drop behind enemy's back. And you sure want some of these, for strategically critical missions. These missions may be suicidal, but that's the duty sometimes.

Urban war

In dense urban areas, you don't see opponent until he is one or two blocks away. For mech, this is a few steps distance, and at such a close distance sword can be more efficient. Time needed to slash is shorter than time needed to aim a gun. And with gun, if you miss you are destroying infrastructure your side will need, a problem nonexistent for swords.

Shield Technology

Technology exists that can protect against small projectile weapons, but not against the much larger force and energy that comes with the swing of a melee weapon(as in Frank Herbert's Dune).

For instance, a mech could be protected by auto-guided lasers that can vaporize small things like rockets and bullets before impact. Or, there's some type of surrounding magnetic braking system that slows bullets down to a speed where they can't hurt the mech. Only A melee weapon swung by another mech would have the energy needed to make it through the magnetic field.

Hence, it would be necessary to outfit the mechs with large, sturdy melee weapons to destroy each other with.

Why would giant Mechs use melee weapons?

Actually my answer is more for this question "Why using giant Mechs in the first place?"

Answer: Demoralisation

The party that uses the Mechs instead of conventional weapons has high advanced tech and wants to show it. Their Mechs are so advanced, that they can easily compete with Tanks of other parties and outperform them.

Everyone knows how dangerous these things are. With the height of a small building they can be seen and more important, better identified than tanks.

The tactic is to lower the moral of the enemy. Taking advantage of the fact that you are there and everyone knows it.

Now we come to the part why using melee weapons

The Mechs should be able to get in close range to their target in a short amount of time. The longer that will take the more hits it needs to evade or absorb before doing anything. Actually I don't know how good tanks are in close combat, but I assume that they perform not as good as on distance. Everything that explodes would also harm the tank. Maybe the turret can't aim at the Mech because it is to close. The disability to attack the enemy with full efficiency could have an even more demoralizing effect.

So the reason to use mechs is not because they are better in combat, but to strike fear to your enemies. You could make the mechs bigger than trees and houses. So advancing enemies will definitely see them when they stand up in the woods.

In the end the mechs exists to prevent fighting in the first place. No one wants to fight the mech.

Momentum

If mechs have extremely strong armor then you need to deal extreme damage. You can't kill an elephant by pocking him one thousand time.

You need a ram (call it a spear to sound more noble) with the momentum of a mech behind. This will have much more momentum or kinetic energy that any kind of bullet or rocket.

To be a bit more scientific, there are mostly 2 reasons a ram can deliver more impact than a missile:

delocalized burner

A rocket can only deliver as much kinetic energy that it can afford to burn in its travel time. If this power gets too high, the engine burn or melt. Same problem with a canon.

The engine of a mech has the same constraint, but it has one engine for each join and can afford a complex cooling system. Hence a mech cool MUCH faster and can produce more energy over any given time.

Aerodynamics

Aerodynamics is on the melee weapon side (maybe on the rocket's, certainly not on bullet's)

To deal extreme damage a missile need to reach extreme speed... but then have to face extreme air resistance.

A very large mass with a lesser speed do not have this problem.
A 100kg Warhammer slashing at 200 m/s is possibly more realistic than a 500g bullet at 2800 m/s (10 000 km/h) and have the same kinetic energy. And a 10t mech need only 20m/s to reach the same energy.

You can increase this by setting you story on a high density atmosphere. Or even underwater

Serious radar jamming technology

Take a note out of Gundam, one of the pioneers of the giant mecha genre. Wanting to write a plausible humongous mecha story but realizing that giant humanoid combat robots are pointless and impractical, the author created a world where a newly discovered particle made radar jamming easy, rendering long-range weapons useless against mobile enemies. Also I think it made problems for delicate equipment and computers. So human-piloted humanoid mecha fighting with melee weapons made sense.

Same reason knights in medieval battles carried daggers;

As a backup weapon, and for utility.

Battlefields are unpredictable, and no soldier will want to go into a situation where they might have to fight against someone who will have a total advantage. Imagine trying to direct ungainly arm/weapon pods of a mech while ducking and weaving at an enemy whose only a few feet away from you and doesn't have that limitation.

Molot makes good points about ammo conservation and the cost of shooting things, but if you're going to build mechs anyways, I feel cost can't be TOO much in the forefront of your mind.

An enemy mech that is melee equipped only has to swing his arm in your general direction when engaged at that range. If you get hit, even if it doesn't do much actual damage, your knocked about; your facing is probably changed, and your mech might very well end up on its butt and out of the fight. And, as with knights, someone quick and with a dagger was a real danger; they could get around you and shove it into one of the weak points of your armor quicker than you could turn to face them (especially) if you were bogged down in the terrain and they were not.

Melee weapons grow in effectiveness if the ranged weapons (guns, lasers, missiles) require multiple hits to penetrate/kill. The longer it takes to down the other person, the more chance they have to close that distance and knock you off target.

These type of encounters WILL happen in a limited visibility environment if both sides employ high mobility mechs; cities, fog banks, dust and rain storms. This is more endemic of warrior style combat then soldier style, where individuals and small groups engage without support, but is perfectly reasonable for commando style fights.

Another major factor is the utility of melee weapons for mechs. Maybe your “sword” is in reality a giant shovel; its main job is to dig trenches and help construct a forward operating base. Even current soldiers digging tools (E-Tools) can in an emergency double as a melee weapon. Knights used their daggers off the battle fields for various tasks, including to eat with, and while probably not ever expecting to have to use them on the battlefield, took them anyways because “just in case”.

Can I recommend the Battletech universe as a reference? The entire system there revolves around mechs of one form or other. The major reason for using mechs in melee fights was that they weren't battlemechs. Many common mechs were construction, lumber or transport mechs, which wwere retrofitted for combat. So, lumber mechs had their chainsaws, construction mechs had mechanized hammers and so forth.
The actual battlemechs had no melee weapons, whatsoever.

However, I can think of a couple of tactical needs for bothering with melee weapons. As I pointed out in my earlier comment, any sort of interference with sensors, with some sort of terrain obstruction--be it fog or a steep mountain would mean you can't see the enemy till they're right on top of you. Since the sensors don't work, you can't risk sending tanks into the fog for fear they'll get stuck, unless somebody opens up a hatch in order to guide the vehicle--and then they'll be sitting ducks. That's when you send in mechs armed for melee combat. The mechs can cover any kind of uneven terrain better than a wheeled or tracked vehicle can, the transparent visor means the pilot can see where it's going without having to pop their head out. And most importantly, if they do see an enemy vehicle or mech, since they'll be right on top of them, they can respond immediately, without having to fall back in order to aim.

Bad sensors

Range weapons require you to be able to accurately detect the location of you opponent in real time and have weapons able to hit him.

You could have situations were sensors are easy to jam or that there is snow or ash falling that blocks site more than a few yards away. Frequent use of emp would kill sensors as well, so if you have to wait till a foe is a few dozen yards away you might as well use melee weapons.

Unstable platform

A biped walker is much more unstable when walking than a tracked or wheeled vehicle, this will make the weapons they fire less accurate at range, again encouraging close range.

Durability

Humans are odd if you punch a thumb sized hole basically anywhere in them they can bleed out and die quickly without treatment. But a mech could survive dozens of holes in limbs and keep fighting, it could have valves to cut off the flow of oil or electricity to damaged sections and so survive and keep fighting despite the loss of 3 limbs. It would be hard to dismember a mech completely enough at a distance to take it out of the fight (basically punch small holes in it till it stops working). It might be faster to attack it in melee (cut large slashes in it) (especially if you have light sabers) Robots survive better than humans if small holes are punched into them so gun fire might not be the best way to destroy them.

Why do humans that carry a machine gun still carry a knife, a sword like in japan, or an axe like the Indians and vikings did.

I'd say as many already have ammunition. It can run out, it weights a ton.

But the foremost reason I'd use a melee weapon in combat over high explosives, nuclear bombs, Plasma bombs and other explosive devices including mines is proximity and precision.

Do you really want a nuclear bomb to go off near you even if you have centimeters thick composite armour when another mach stands near you? No you take your knife and find the weak spot in the armour.

Personally I would like a spiked club that is electrified. he he

Extreme close quarters combat. I'd note a 'traditional' mace or axe would be a pretty terrible weapon on this situation. A Jackhammer the size of a small truck on the other hand, might be more useful in short range combat. Unlike a gun, you can power this off the same power supply as the mech itself, and it would be useful for combat engineer type work, demolishing and building fortifications and so on. After all, hitting someone in the head till they stop moving is a valid combat tactic.

Likewise a high speed spinning blade might make more sense than a sword. A sword against armour might stop. A high speed blade would slice through.

And similar weapons are in use in robot fighting tournaments, so you might have a 'in universe' explaination of pilots being familiar with such weapons - you'd have 'military' mechs with mainly energy and projectile weapons and 'gladiatorial' mechs that combine top notch pilots with limited armaments and physical weapons.