I installed the Beta patch, since I read that it included the DX9 fix.
I'll try buying a new ship. I also noticed that sometimes after restarting the whole game, it will kick off the time again, but only for a while, then it dies again.
I moved all the way through Romulan space, avoiding any contact, from the left to the right and back again and the time did not restart. Then I did some missions, time did not restart. Restarted the application, time restarted, went through turns, stopped again.