1996 rodeo a/c fan?

MY 1996 RODEO A/C COOLS GREAT UNTIL DAYS

GET REAL HOT. THE A/C FANS STOPS AND I GET WARM AIR. AFTER IT SITS FOR A WHILE, IT WILL PROPERLY AGAIN. WHAT MAKES THE FAN STOP AND START?

the compressor turns the fan on and off when the fan shuts off see if the compressor is still on if not you probaly need to replace the a/c cutoff relay .if compressor comes on and off alot compressor may be low on freon.hope this helps.

If both the compressor and condenser fan stop (at the same time), something in the control circuit is opening. Try cleaning the condenser since a dirty condenser causes high pressure which opens the high pressure control.
If only the condenser fan stops (and the compressor might stop later), either you have a bad condenser fan motor that is tripping on thermal overload (marginally worn bearings) or a loose connection. (Note that the condenser fan motor and compressor generally share a relay. There’s an exception for heat pumps or A/Cs with head pressure controls, but you probably don’t have either one.)

Question first. By a non-working fan do you mean the cabin fan, heater fan, or whatever you want to call it?
Is there no air coming out of the dashboard vents?

Trying to decide here if you’re suffering from a freezing evaporator or not.
Next time it does this, stop the vehicle and look underneath approx. where the passenger’s feet would be.
You should see a slow water condensation drip there.
If not, turn the A/C off, heater on, and check again in a few minutes.
If water starts running out then the evaporator is freezing.