Why does my 1996 jeep die at stops when air or heat is on

Could be a sticking idle air control valve, or dirty throttle body.
The computer uses the valve to control idle speed by regulating the amount of air into the intake.

Hi, first check for a clogged PCV valve. This can cause your idle air control valve to act up. The pcv valve is shoved in to the valve cover with a hose on it that leads to the intake manifold. If the PCV flow is good, check for vacuum leaks on any hose leading to the intake manifold. Do you have a performance chip installed on this Jeep?

Do you have the air filter in place? The removal of the air filter will cause this same issue. If it is not the filter, then the mass air flow sensor could be going out.

Try removing your a/c heat unit unplug it make sure all contacts are clean reconect an check, this has work for me on a few dodge vehicles with likely problem.

Check out your cold start choke. It is designed to cause your fuel mixture to run "rich" until it warms up. It is basically a heat sensitive coil that reacts to heat from the exhaust manifold.

have you looked at the plugs

does your jeep run rough? idle is real low? and when you are driving and push the gas hard it doesnt want to move? if so it is most likely the mass air flow sensor. i had to replace that 2 or 3 times on my 1999 jeep cherokee

look for vacuum leaks, especially around the air boot

Sounds like fuel starvation.
Check fuel lines for leaks/blockages. I don't know your motor and even if it has a carburetor, probably fuel injectors which are a common weak link in some cars fuel system.

If carb the air fuel mixture ratio has to be correct
With injectors these can easily become blocked and may require a trip to the garage

The most basic thing you could check is your air filter when did you last change it. Always start off with the simple and cheapest things before spending cash

My 2000 Grand Cherokee had the same problem, without all the sputtering, it would just die approaching a stop. We could only keep it running by slightly pushing down on the gas petal when coming to a stop. I replaced the Throttle Position Sensor, but that didn't change anything. A new mechanic I found replaced the Idle Air Control Valve, and we've had no problems in a week.