Sounds like the torque convertor clutch is getting hung up.

Given the age of the car, you might want to try disabling the lockout feature; perhaps if it does not lock up it won't stick. I had a '94 Cavalier which had the opposite problem, at low speeds it would not lock up, I put in a switch to cut the lockout out, I would then switch it in at a relatively high speed. The lock out is controlled electrically by the ECM, and you can just cut the wire to the Transmission to disable it. BTW I eventually got about 210,000 miles out of that car.

what color is the transmission fluid? When this happens it often means end of life dur to burned clutch particles clogging the hydraulic logic in the transmission.

How many miles on it?

Your car is equipped with a lockup torque converter. What is happening is that the lockup clutch is not releasing and when you slow down it drags the engine speed down and stalls the engine! I have seen this problem several times and it can be cured by replacing the sensor/solenoid that locks and releases the torque converter.

Exactly,

But prepared to get sticker shock for the repair.

Check this thread,

http://cr4.globalspec.com/thread/34542#newcomments

Joe

I'm no expert but it sounds like your lock-up torque converter is not disengaging assuming you don't have an engine problem. I assume that when you put the car in neutral the car will run even after the 30 minutes? I say this to eliminate that the cause could be an engine problem.

Like many above it is the TCC Solenoid this can be found on the drivers side of the vehicle behind the end cover of the transmission. If you are handy with tools you can replace this yourself.

A way of testing to be sure if it is the Solenoid, is to unplug the square plug on the front of the transmission near the top. If you unplug it and the problem goes away it is the solenoid. you can run like this for a short period of time but its not recommended and it will eat up your mileage.

Remove the drivers side tire and you will see the end cover. Remove the end cover and at the bottom of the valve body you will find a small solenoid. R&R that solenoid and reassemble everything. There are a couple of wires that you will have to hook up in the right place but its really not all that hard.

The solenoid is less than a hundred bucks and the gasket is about 20 bucks, it takes about an hour and a half to change it if your good with working on cars.

The above post is correct, but you can simply disconnect the TCC by unplugging it. It will have a minimal effect on your mileage and I ran mine that way for many thousands of miles with no problem.