Engine turning on and off

How rapidly?

 

If your Prius is warmed up and the HV battery is fully charged, that is the expected behavior. The engine shuts down at a stoplight to save gas. It then starts back up when needed to provide acceleration. If you just accelerate slowly, the engine will stay off as the HV battery/electric motor can supply enough energy on their own.

JeffD

 

I'm going to assume that you mean that the engine will turn itself OFF at a stop and then back ON again. How are you determining this? Are you looking at the power-flow diagrams on the MID or feeling the engine vibration and listening to the exhaust tones?
If you have a weak or dying traction battery, that would probably happen. Next time this happens, look at how full the traction battery is. If it's at least a quarter full, the engine should stay off at a stop - otherwise the engine will fire to maintain a minimum charge level on that battery.

Hope this helps.....

 

OP has never been back to say how rapidly....