Car is slipping into neutral sometimes when I come to a stop

I have a 97 Plymouth Neon with an automatic transmission and lately when I come to stop the car will automatically shift into neutral. I have to shift into another gear and then back into drive to get it to go again. Could I just need new transmission fluid or is this a more serious matter?

Odometer mileage?
Date and odometer mileage of last transmission fluid change?

It has 125,000. Last transmission fluid change was 05/05 at 92,000 miles.

Well, it sounds like you are reasonably up to date with maintenance, so I assume that you have already checked to be sure that there is adequate fluid in the transmission. If that is the case, then you might want to try a fluid change, but you have to be prepared for the possibility of more serious problems.

A visit to an independent transmission shop (NOT AAMCO, Lee Myles, Cottman, Mr. Transmission, or any other chain) should probably be your next step. If we are lucky, our resident transmission expert, Transman, will log in to give you some specific guidance here.