Car had to be jumped twice in past week. New battery.

#1
Hello all! This is my first post; I'm excited to join the community of Corolla drivers!

I have a mechanical question about what could be wrong with my Corolla.

8 days ago my car wouldn't start. So I jumped it, and found it odd, but it seemed to be running fine. So I kept driving it and for a week it worked fine. Then yesterday (a week later), it wouldn't start again. So again I jumped it, and again it has been running fine. Obviously, I'm concerned as to why this has happened twice in one week, and afraid it may happen again. I replaced the battery with a new one from Advance Auto Parts about 6 months ago.

So I thought I'd start with the battery or alternator. I took the car to the Advance Auto where I bought the battery, and they tested the battery, alternator, and starter. They said the battery looked okay but was not fully charged. They suggested I leave it with them for two hours while they charge it, then they will test it again for a final reading. They had some machine hooked up to the car and had me rev the engine, turn on lights/highbeams, turn on heater, turn off lights and heater as part of the testing. They said the alternator was good, and the starter was reading 11, when it should normally read 12, but said 11 should still be enough so they didn't think that was the problem. I came back 2.5 hours later and they said the battery was now fully charged and tested good. As a result, they would not replace my battery under warranty, and said they couldn't do anything else.

So now I am with a car whose battery and alternator are 'perfect' with a slightly weak starter. Any ideas as to why the car needed to be jumped twice in the past week? I had thought it was the alternator which I figured would explain why the car worked for a week in between until the battery fully drained again. Could a weak starter be the reason the car wouldn't start? In other words, the battery was strong enough, but there just wasn't enough crank in the starter to get it to run? And then putting jumper cables on made the starter strong enough? Sorry for my rambling, I'm just a bit confused.

Thanks to everyone in advance!
 
#3
I should have added. It is an 05 Corolla with 50k miles.
It could have a short somewhere which drains the battery while it is just sitting there not running, draining the battery. If the starter is at 11 instead of 12 (whatevers ..amps?) then it might be somewhere near or in that. Short circuits are hard to find but there might be a tester or "OBD" which could help. Sorry I don't know more.
I have a 2005 Corolla with weird electrical problems including not being able to turn the engine maintenance light off from blinking 7 times upon start up and other nagging issues. I've changed the oil, done all the suggestions with odometer. Nothing in manual and I don't have the mythical "supplemental owners manual". 110K miles, runs great.
 
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