Assuming you didn't get unlucky and buy a dud for a battery, my first thought is that the alternator is not sufficiently charging the battery while she's driving around. I know there are various issues that can go wrong regarding alternators, but I'm already at the limit of my knowledge.
Electrical problems can be hard to track down, and you may need a mechanic to do some testing. As some Audis are known for having electrical problems, I'd find a mechanic specializing specifically in Audis or at least in German cars.
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