sounds like the torque converter needs repair.take it to a good transmission shop
Try changing the fluid and filter.
Low fluid pressure, sticking checkball, worn clutches......these are some likely causes
If it a manual transmission it could be fluid level/needs changing, shifting fork/linkage or syncro issues. If it is an automatic, the fluid level/condition can affect shifting, also if the valves in the valve body are sticking. The transmission can also just need rebuilding, clutches are worn.
If it's an automatic, you may have a sticking solenoid INSIDE the transmission.
A very low idle can cause a 97 Ford Taurus to stall. Another reason for stalling may be transmission bands sticking, which does not allow the transmission to come out of gear on idle.
if it is automatic the transmission could be slipping if manual the throttle could be sticking
EITHER NEEDS LINKAGE ADJUSTMENT OR TRANSMISSION OR MOTOR MOUNTS COLD HAVE SHIFTED.or wrecked.Or THE DETENT in the trans is sticking
Most usual reason is the ignition module in the distributor, or it could be the float needle sticking if it is the carby model.
Automatic trans. on Neons used to have problems with the solenoid packs sticking. Check to see if you have a transmission controller code. If it has a code for L/R solenoid stuck in L or R poistion, put a solenoid pack in it. It might just be that the trans needs to be overhauled.
sounds like one of the valves in the valve body is sticking when it gets hot (metal expands). Sounds like a Ford automatic overdrive to me.
If the idle is set too high, and you have an automatic transmission, this will happen. A sticking throttle cable or rod can also do this.
The transmission "valve body" can often have problems that result in leaks and sticking. Once the seals of a valve body start to fail, the transmission clutches start to slip and eventually fail altogether. In any case, once the transmission fails in the way you describe, you're pretty much stuck with the only options being to rebuild the transmission, replace the transmission or get rid of the vehicle.