the roadie is right. Diagnosing exactly what and where is draining power will ultimately try your patience, but to confirm that it IS a parasitic drain (seems very likely, though, doesn't it?):
1) get a cheap multimeter, probably even the one from harbor freight for free some months and $3 others will do if you won't need it much, or get a $100 one if you think another day you'll be testing voltages on computer circuits, but you won't need that to find your drain.
2) make sure everything is off, all lights, and with the hood up and the hood light (is there one in a trailvoy?) unplugged to eliminate that draw too, unhook the negative terminal and put your multimeter set to amps in there.
3) someone else help me out here; there IS going to be a normal draw for the sensor that's constantly on, listening for your key, and for the computer RAM that stores the clock and radio stations, and maybe saved seat settings but I don't know. These are low, low draws that would take weeks and weeks to kill a battery. I don't know what's normal for the trailblazer, but I had to troubleshoot my old ford once (found a shorted wire in the tailgate, sheet metal had cut through the insulation from years of rubbing), and normal for that car was .07 amps. It was an older vehicle, a trailvoy will probably be a higher value.
If you're seeing like 1 amp, you've got an issue. Not that you can't already guess it, but, nice to be sure.
4) Now the time consuming part, which component on which circuit?
I'm not very experienced nor very good at fault tracing, so if someone else has a better method, PLEASE chime in,
But what I did was to remove fuses one at a time and with needle probes on my multimeter set to amps, probed across each fuse slot one at a time. Because the dome lights were on because my door was open, I made note of which fuse that was and ignored the amps running through that circuit.
Alternatively, with two people, one person can just leave the ammeter at the battery while you're pulling fuses, and watch for the amps to suddenly dip when you pull the fuse with the short on it [or the dome lights
], and then you've found your circuit. I think the trailvoy has a couple fuse boxes, one under the hood, but another under the front seat or something?
Then look up the electrical diagram for that fuse, and individually test the components that run off of it.
When you're done and it's fixed, consider getting a new battery. Deep draining is seriously not good for them, and if it's happened several times now, it's going to be toast sooner than later.
Physical reason why is that you've got metallic lead converting to ionic lead (sulphate?) in solution when you discharge, and then back to metallic lead on the plates when you recharge. But having been deep-discharged, the lead never reforms onto the plates quite the way it was before, and cold-cranking amps --directly dictated by the surface area of the lead exposed to the acid bath-- are forevermore reduced. When all the lead has left the plates when deep discharged, and then reforms again, it will not be as spongy and not nearly as much surface area as it was when the battery was new and charged. Come winter you may have trouble starting in chilly mornings.