I have found most of the time a severe drain on the battery that will kill it in 1 or two days is the internal rectifier in the alternator. I beleive GM refers to this device as a diode trio. It allows current to flow one way only. If it is broken it will allow the alternator to constantly drain the battery when not being run.
I would bet on the alternator, but if you've killed your battery several times, it will also be weak. A car battery isn't a deep cycle, and they don't like being drained completely.
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