2008 Prius with possible 12 volt battery issue

I have a 2008 Prius and replaced the 12 volt battery in April...my son has been driving the car for a year while at college. Anyway, he has graduated and is now about 5 hours away where he now has a job. In early June he would occasionally get some beeps after turning the car of...it did this before the 12 volt battery died in April. No warning lights would come on and it wouldn't beep all the time. (He did replace the batteries in the fob) I went up and traded him cars to have it looked at where I live. It never beeped for me until I went to leave the car to be looked at. They couldn't find any problem and there where no error codes. He called me Friday saying the car wouldn't start. He had someone jump it and he brought it back home. Did we get a bad battery maybe when it was replaced at the dealership? Any ideas on what could cause the 12 volt battery to die after only 2.5 months? Just looking for some idea on what could be going on. Thanks I'm going to call the dealership in the morning

 

Right now the car has no power...have to use the key in the fob to unlock the door. If I turn on a map light it is VERY dim.

 

He keeps,the switch for the auto light for the doors in the off position so I don't think it's the lights.

 

Ok, I'll try that in the morning. Thanks

 

One thing I noticed in the video is that it said the "triangle" would come on at start to indicate a possible issue. In this case this never happened. The only "odd" thing we'd experienced was a beeping every once in a while when turning the car off and getting out. This what happened when I took it to be looked st about a week or so ago. My son said when it'd do this if he turned the lights on and of it'd stop the beeping. Sometimes he'd have to do that a couple of times. Could some component be drawing power that would show up in an error code or a warning light on the dash?

 

Well, jumped it this morning and let it stay in ready mode for over an hour and then ran the diagnostics here are images of what it read...






any ideas what could be the issue? It looks to me like the 12 volt battery is reading as being ok.

 

I took it to the Toyota place I bought it from. Although they had to jump it to pull it in the bay, they claimed there was not issue. All their tests showed nothing. So I've had it at home and from a guy I know who was a Toyota specialist as a dealership, I let it sit for 3 days. Checked the voltage yesterday and it was at 11.9. Checked it this morning before I drove it and it was at 11.4. Once I got to my office I checked it again and it was down to 10.8...called the dealership back and talked to the same guy explained what was happening. I'm bringing it back this afternoon. Any ideas?

 

I don't have a voltmeter (I do plan getting one), but I used the diagnostic mode without turning the car on (without pushing start with foot on break). They guy I know I've talked with said it could be something related to the smart key and the door sensor...but he also said it could be a lot of other things as well.