A bad starter will not cause an engine to stop while driving. A common problem that will cause the engine to stop running, or not start, is a bad CPS Crank Position Sensor. It's also typical that after it cools it will start working again. You can search the forum to find many threads on this. Most everyone will highly recommend that you use a Bosch CPS replacement.

Another cause is a bad RCM Relay Control Module. Here is a link to a long thread on it:

https://www.crossfireforum.org/forum...-no-start.html

I experienced both problems at different times with my 2004 coupe.