Battery Issue, engine quits.

OK...I hope I have posted in the correct place. 2011 Prius 52,000 miles. 12 Volt battery died, replaced with a new battery from Toyota. The car will start with the start button held in. It will run for a few minutes and then die. Curiously it will start again if the gas pedal is firmly depressed. This is the second time I have had this issue, last time was two years ago.. Last time the vehicle was towed to the dealership and fixed within an hour. Total charge was 90.00 so it was not major. I never got straight just what was "reset". I have tried an electronic reset by disconnecting the negative to the chassis. I have also checked the HV disconnect. The hybrid battery indication is charging while the engine is running. What am I missing here?? Any suggestions would be appreciated!!! I do not have a code reader.