Sounds like a bad HVAC programmer issue, but there could be an electrical problem, such as a loose/bad ground that could cause this. This has been an issue with the automatic climate control systems for a while, but the later cars, such as your '96 should have had all the bugs worked out of it.
Perhaps someone else can narrow down the possibilities...
You should have someone scan the system for codes, and see if there are any that lead to a particular problem/area to check.
You can check for codes by pressing the fan UP and DOWN buttons at the same time, and hold them down for about 5-6 seconds. Watch the display on the cluster(where the mileage reads, or on the A/C display...I don't remember), and it should show -00. Then press the fan AUTO button. Any trouble codes will show in the LCD display. Check that, and see what codes it has, then post them here...

Welcome to C4VR, tho!!
Adams' Apple2009-05-28 10:22:22______________
Joel Adams
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"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"