I will admit electrical is not my forte, but.... I would start by having the battery tested and make sure it's holding charge... If it's not the battery it's likely a small current drain somewhere. With the key out, start checking for current flow thru the fuses... (pull the fuse and read current between the sockets) I'm not very good with electrical and I can't remember what expected for total current drain. I think like 300-600 milliamps (.3-.6 amps) is expected, but I'm likely very wrong with those numbers. Hopefully someone else knows better numbers. If you find one that is drawing current then you have a starting point for finding the problem... (In my experience it's usually some sort of convenience light (in glove box, trunk, ect) that is suppose to turn off automatically but isn't.)
I have the same type of electrical problem(s) with my 2001 Blazer. It looks to be a common problem. Fusible links, crank position sensors, alternators, ignition switchs, etc. All are possibilities for the culprit, yet usually it's a good battery. There must be a common thread somewhere with all of these failures on this poorly designed circuit(s).
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