I've never done this but I know for a fact that motor armatures are precisely and tightly wound. I don't belive your method would do the trick. Someone correct me if I'm wrong but the armature coils are soldered in and just rapping around some more wire would do more harm than good. For now, I would just clean out the motor with a good electronic-safe solvent and oil all the bearings/bushings.

I'm pretty sure you're correct. Motor armatures are very carefully wound and wrapping more wire around it would probably decrease the power. To change how much power the motor has by changing the armature you have to re-wrap the coils with a more conductive wire. Also, I think the wire has to have a special coating for insulation.

Yes the wire used inside of motors is specially insulated with varnish. If this is nicked in anyway it can short out and burn up the motor. I would assume that you have an AC motor on your air compresser at home. One you plug into a wall outlet. These do not have armatures inside they have rotors. The motor is wound in different phases and in specific spots around the stator. It is possible to wind more wire inside the stator but you would have to know exactly how the motor was wound to begin with and what the wire would do to the motor. And more than likely you don't have the wire to wind with anyway. Plus there won't be any room to add wire. They don't have any extra room inside motors.

What kindda problems are you having that you need more power for your compressor? I work for a motor manufacture. I might be able to help with your problem.

Well it's an old compressor (I snagged it off of ebay for like, $30). I want to get 25-30 psi out of it, but right now am barely getting 20.

if you know that HP, max rmp, amps, volts, etc and look up a new on the internet. They may not be that expensive you also may find one at an auction. If it's really old the bearings may be shot. You can try freeing the up. If you can take the motor apart and clean it that may help.
Does the motor stall?? If it does then I would say it is the motor if it doesn't then you may need to look at the piston or snap valves and make sure they aren't bad.

Joe,
There are a few problems to address...
The motor was already carefully wound at the factory and unless something has gone wrong with it since there is not a lot you can do to increase the output power. By changing the windings (adding wire)you affect a variety of other variables like balance, heat dissipation, etc. If it is an AC motor (as stated above) then you will change the load the motor presents to the line (electric company) or in the case of a capacitor motor will affect the current and phase supplied to the motor windings, generally reducing power not increasing it.
If the compressor was originally designed for higher pressure there is often a mechanical reason for the poor performance. Usually these are faulty piston or rings, leaking gaskets and fittings or bad over pressure regulator. If the compressor is getting up to 20 PSI and shutting off, then the limit switch may be adjusted for a lower pressure.
In general for our robots, the specifications given for each of the motors allows mechanical designers to use each motor with predictable results. The engineers may choose to run the motor at points on the curve that may not be the most efficient but optimize one factor at the sacrifice of others. That is one of the nice things about this competition is that your hands are not completely tied by the rules.
Hope this helps...

Anything is possible
 

It is possible the rewind motors, but is NOT ALLOWED. HIGHLY ILLEGAL and it is not is the spirit of gracious professionalism.

Just as a acedemic exercise: I knew a machinist that helped his son race RC cars. With the correct winding equipment and KNOWLEDGE, the motor can be rewound with SILVER wire. Expensive compared to copper. The result? The real resistance of the motor goes down because silver is more conductive than copper. The motor will also operate cooler due to less I2R losses.

Just and interesting tid-bit for future years.

I agree that the resistance would go down, but by an imperceptible amount. Silver wire of the same guage has about 94% the resistance of copper. A motor winding of copper at 10 ohms would be reduced to 9.4 ohms in silver. For our purposes (ignoring the other factors that affect motor current) Ohm's law suggests 12volts/10 ohms=1.2A and 12 volts/9.4 ohms=1.27 amps. When you throw in the other factors there still isn't sufficient evidence that would warrant the change. Yes there is an increase in winding current which results in an increase in magnetic field, but if the magnet structure was already optimum, increasing the electric field does not result in higher power. The increase in motor current also produces changes in power dissipation. Again ignoring other factors Ohm's Law for power shows 1.27 amps^2 x 9.4 ohms=15.16126 watts and 1.2 amps^2 x 10 ohms=14.4 watts so there is an increase in temperature due to the higher current.
And yes there are a lot of other factors to consider in the scheme of things.
In the case of our new drill motor the change in wire would result in a stall current of 138 amps vs. 129 amps and 1657 watts vs. 1548 watts dissipated at stall.