Q: Why would make my car keep dieing and draining my battery? on 1991 Buick Century

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I replaced the battery and alternator in it
(2) Answers
Sounds like you have a draw on the electrical system causing the battery drain. Typically any tech would suspect the alternator and would test that first. What did you replace the alternator with? Used, new, reman, rebuilt, did you do it or a qualified tech?
same problem in a 91 Custom, we just ended up pulling the fuse for the clock. you just will have to take it out every time you are not driving. This was the cause of battery.

It must be a blown fuse or short in the electrical.