2012 VW Jetta GLI Battery Dying Constantly -- No One Knows How To Fix

I have a 2012 Jetta GLI thats had it's fair share of issues, but none this
irritating/costly! About 3 weeks ago I went to start my car and the battery
was dead. I figured this is probably routine maintenance as my battery is 5
years old. I called AAA and had it replaced. Car started up and worked fine
for a week.

The next week I start it up and its dead again. Dashboard is lighting up this
time but the info panel on the dash is spazzing out and the car wont start.
So I call AAA to see whats up and this guy tells me my alternator is toast. So
I have AAA tow my car to a local shop to have it replaced. $500 later... my
alternator is changed but the man tells me theres still something wrong with
my car, so he brought it to a Volkswagen dealer down the street...

After being there a few days, they tell me their draw test is showing my radio
is draining my battery. They tell me the only way to change this is to put in a
new radio which is $700. I shopped around but found that all the shops were
charging the same price so I went with VW since the car was already there. I
get my radio replaced, and take my car home. I've been driving it here and
there for two days, but upon leaving for work yesterday, it was dead AGAIN!

I called the shop and had my car towed there again... they sat my car on a
charger all night and this morning all there tests aren't showing any draws
and is saying my battery is PERFECT. The mechanic is suggesting I leave
my car there for a few days to see if it drains again. If it does, they know that
AAA gave me a defective battery. If not, they think maybe AAA gave me a
half charged battery that wasn't able to charge itself fully due to the little
amount that I drive.

I'm hoping thats the case, and since they charged it fully it will no longer
have an issue. Has anyone else had this experience? Does this info sound
right to you? So far I'm $1500 in the hole. :(