On an alpine head unit will leaving a iPod plugged into it drain car battery?

I purchased my truck in january this isn't type of truck Ot brand of truck argument just a concern. It's used the guy before me installed a after market head unit it's an alpine with the iPod cord in the glove box. Once a month my truck battery is dead entirely. The battery is brand new and I actually made them replace it last time. It checkS out good on the battery testers and there is never any amp draw on the battery when I bring it inthe shop while vehicles off. I tried to figure out why's different when I bring it in... I take my iPod out now there's no way I beleive it wud drain my battery but I'm kind of wondering if leaving it plugged in is making the alpine stay on in some way?