electrical/cruise problem? car stops responding to accelerator, have to power off and power back on

My opinion only, but I think 11.5 is marginal at best. A healthy 12 v car battery should never go below 12v, especially since a Prius battery doesn't crank the engine, but is only used for auxiliaries

 

Toyota said that? Without plugging in Techstream and reading the trouble codes?

That should be step one. When those lights come on, that means there are trouble codes that have been logged in the car's computers, and they are severe enough to trigger the self-protection mode that you keep overriding by power-cycling the car. It may not take long to compound the damage that way.

What you think of as the systems diagnostic screen on the center panel is mostly for the entertainment and nav if you have it; it does not have general access to diagnostic codes from all the car's computers. That takes plugging into the diagnostic port, something Toyota should have done right away, before waving their hands and guessing.

-Chap

 

A soft 12 volt battery does not make the car shut off during driving. During driving its on the dc-dc converter and the system is seeing the charging voltage which is usually around 13-14 volts. You can disconnect the battery while the car is running it does not care.

11.5 volts on a 12 is very very low but still has enough power usually to boot up a Prius.
My own oem battery was 11.5 for quite a while.
If it falls below 11.2 volts the dash will throw a big red caution sign momentarily on boot up.
That's the only warning you get. It's quite noticeable as it's the only light not used in ignition bulb check routine. I saw it on my car when my soft oem finally cratered 7 years later.