2003 Chevy Trailblazer New Battery going dead

Welcome to the forum, I looked through some service bulletins, didn't notice anything particular. I'd look for lites left on, under the hood--interior-- luggage area, best time to check is in the dark. General info says battery draw no more than 30ma, that is no where close to half amp. If all else fails, check the amp draw, pull fuses one at a time, when the amp draw goes to normal, the problem circuit should be on the fuse circuit you just pulled.

I'd also have the charging circuit checked.