PLEASE HELP: 1997 Mustang Power Drain Issue

Hey guys, wondering if anyone could help me out! I have a 97 manual mustang which I love, but I am having a major issue! After about 3 hours of leaving it after driving, the car completely looses power and the battery is completely dead. Its also done this a couple times when driving. I have a feeling it may be the battery because it is a remanufactured battery, but I wanted to ask you guys first. Yesterday the car died in my driveway and when I tried to jump it (given the car jumping me was a tiny little rice burner) the car couldn't even draw enough power to start. So now its just sitting in my driveway dead.. What do you guys think, Battery issue possibly alternator?

Side Note: Passed emissions fine, showing no codes, mechanic said it was fine, no other problems except for a loose muffler.

Symptoms:
- Car looses power when sitting sometimes (rarely) when driving.
- Cars battery is completely drained, won't draw enough power to jump.
- Car has done this multiple times.
-Now fully dead in driveway

Help me out! thanks guys.