Mitsubishi Repair: 91 eclipse battery problem, eclipse gsx, drive belts

Question
91 Eclipse GSX AWD turbo 2.0

i have been having a problem with losing all power in my eclipse.  one day at work i left my park lights on like an idiot so the battery went dead.  we jumped it and got it started a few times but after about 10 minutes it slowly fades all power away and is dead again.  charged it overnight and it was good for about 35 miles then the same thing.  the door "beeper" sounds choppy, the electric seat belts work only when it is running, door locks dont work together anymore, radio turns off everytime i touch the brake.  i was told it was probably a battery problem and these problems were common.  I got the alternator tested and it checks out good.  Bought a new battery and thoroughly cleaned the top mount connections.  We wired the battery different and it doesnt turn off anymore.  door locks work but seat belts still act funny.  door beeper is still choppy. Since i installed the new battery it went about 50 miles before slowly fading away power again.  any suggestions? bad wiring, or poor battery cables? thanks for reading
Travis

Answer
Travis,
I'd still lean towards a faulty alternator as your problem.  I've had my alternator on my 90 GSX go bad a couple times and the symptoms you described were the exact same as I had, which turned out to be a direct result of a bad alternator.  If you're stiil using your original alternator, then it's probably due for a replacement.  The alternators in these cars last about 10 years, and typically do give a far amount or warning before they completely fail.  

Also check your drive belts and have them replaced if they've been on your car for more than 60,000 miles.  If replacing the alternator and belts does not help, you probably have a grounding problem or other wiring problem.  You may need your battery cables replaced as well.
Good luck!