1991 Dodge Colt Stalls

After driving in one direction for about 15 miles I have no problem. I shut the car off go in a store and start the car back up. I'm going down the road and 5 or 10 miles later the car just stalls. I try to pop start it and it NEVER restarts when I attempt that. ONLY after I come to a complete stop am I able to restart it. Sometimes I have to wait a little while (maybe 1 minute at the most) before I restart it with the key and off I go a few more miles and then it happens again. So far I've tried the fuel filter but it was in vain. Any ideas? Anyone seen this before?

a little history on the car would help /motor ???? trans/mileage??? how long you had it ???? what has been changed and in how long ??????????????

it could be cheap or expensive.

if you live within a 10 hour drive of dallas tx i will come buy that car from you.