It's not on a Grand Prix, but a 3100 equipped 03 Buick Century

Intermittent problem with A/C system ... it works very well for first 15-20 minutes of driving. After this period, it will periodically switch from cold air to ambient temp air, almost like the system is shutting off. A/C light stays lit the whole time, and I don't hear the compressor shutting off. The warm air period has no consistency, sometimes it will only last for a few minutes and others it will last the entire ride home. At idle is when it seems to happen the most, when the car is moving it seems to get cold again.

Here's what I have done:

Cleaned A/C condenser with soapy water and pressure washed
Checked cabin air filter and removed all debris around air intake on windshield cowl
Checked A/C pressures in the system .. at 88 degrees outside with 66% humidity the pressures were 48 on the low side and 200 on the high side

My only idea is that it could be a problem with the fans turning off while the A/C is on, this causing the condenser to become heat soaked and kill the performance of the system. What controls the fan operation while the A/C is on?

Any ideas or suggestions are greatly appreciated!