Hello and welcome.
This issues does seem a little odd. I have ran batteries with the radio on all night (on accident) with no problems restarting afterward. It kinda sounds like the dealer is trying to get you to temporary fix a problem so that they do not need to fix it under your warranty. (only speculation) I know that there are some goood dealers out there. My best guess would be maybe your alternator, I believe you can bring it into local parts houses (Napa, Schucks...) and they will test it for free. I believe there is an easier way to test this than just removing the alternator completely, so hopefully someone who knows will chime in. Either way, I encourage you to not give up on your posts as sometimes the smart ones take a few days off. Good luck | 
