What David Hendy said just above. While you're doing that pay particular attention to the soldered attachment points of the wires to the female sockets in the compressor plug. I've seen a few breaks right at this point just inside the plug. Also check the female sockets themselves for loose fit on the male terminals.
Here's some other things to consider:
Check the condition of your belt, belt tensioner, and related components. The belt tensioner is a common problem on '92 models, far less so on the '93 and later vehicles like yours, but it's still worth a check. Any belt slippage resulting in a loss of RPM at the compressor shaft will trigger a protective switch off of the compressor that generally remains in effect until the next key cycle. Do not be surprised if you have codes for this phenomenon in the base module. The problem is that this code is usually present in the base modules even when there is not a problem with the belt drive, so it is not an absolutely reliable indicator.
It rare cases, the evaporator temperature sensor can cause symptoms similar to yours. After a certain period of time, if the control unit does not see a corresponding temperature drop at the evaporator after it has commanded for compressor on, the control unit assumes a defect with the refrigeration system and stops requesting compressor clutch engagement. During these conditions cycling the key will usually produce another 10 minutes or so of refrigeration system operation followed by another switch off.
A poorly performing system, such as one low on refrigerant can cause a similar switching off of the compressor clutch by the ACC control unit by way of evaporator temperature sensor monitoring.
Rarer possibilities include excessive compressor clutch gap, and electrical system voltage fluctuations. Check your battery terminals for condition and tightness. Check your fuses for good connection and tightness. Use extreme care to pinpoint micro cracks at the thinest center part of the fuses and on the cone shaped base ends of the fuses. You may need to physically disturb them to find these conditions.
The condition of the battery and charging system is harder to determine, but if you are noticing any kind of condition to make you think of a battery, say slower engine cranking than normal, you may want to test and / or rectify that condition before you do too much looking for the problem on the air-conditioner end of the componentry.
