Air conditioner Compressor

My car is about eleven years old, and recently the compressor started acting up. Its works fine most of the time, constant gas pressure (no leaks). It works great when it works. Sometimes the clutch just does not engage (when it does it works fine for a day or two). The pressure switch on the accumulator is good too. Everything else works, the current to the compressor is good, condenser fans spin. Engine rpm's goes up.

As I said the current to the compressor is good. But on the compressor there is this black kind of small cylinder, the positive (from the relay) goes in to that cylinder and comes out right next to it then goes to the clutch. The wire going into that cylinder (kind of, its small and black) from the relay has good voltage, but the one that comes out has almost zero voltage. That is when the compressor does not work. Slightly moving that cylinder (it does not move much its almost fixed) causes the positive out to the clutch to go the full 12 volts and the clutch engages (for another twenty to thirty hours).

Please reveal to me the magic behind this witchery.

Regards,
Image Engine