2001 Cougar won't start

[cgia]

My wife has a 2001 Cougar with a V6 engine. Last week she drove from Western KY to Louisville. She turned the car off at the hotel and then come back out a little later and it wouldn't start. The battery was dead. She got it jumped before she left for home and I told her not to turn it off until she got back to Paducah at Sams Club and we would get a new battery. After she turned the car off , we tried to start it after 2 minutes and nothing. So we got a new battery thinking that was the problem. She drove the car for the next four days on short trips of 40-70 miles and no problems. Then went to St. Louis Six Flags and had no problems going there but when we come back out of the park, the car battery was dead again. Jumped it again and got it home to the dealer and they checked over and found nothing wrong with it. They said the altenator checked fine. Oh also before all this the check engine light came on and the dealer said they replace an O sensor.

Anybody got any suggestions?