The problem isn't your batter or alternator or starter then. Start looking into your fuel management system. Possibly your fuel pump, injectors, etc.
it could mean that you have a loose battery cable that needs to be tightened
The alternator belt on a 1994 Eclipse is replaced by loosening the alternator bolts, moving the alternator downward, and slipping the belt off. A new belt is then routed around the other accessories, placed on the alternator, and the bolts tightened.
Your alternator is not charging.
Starting problems in a Mitsubishi Eclipse GST 1995 could be caused by a weak battery or an alternator that does not charge. You might also have gotten a bad starter when you replaced that one.
Bad Alternator, Bad Battery, loose cables
I think your alternator doesn't work properly.
Insufficient charging from your generator (aka alternator).
Maybe there is a short to earth somewhere in the car so the battery is being permanently discharged.
Have the Battery charged and tested to be sure its not over working the alternator.
the fuse regulates the voltage that comes back from the alternator to the battery and system without it you push to much power to the system and it will turn on your battery light and possibly blow your battery and ect....
If you have checked the battery and made sure that the new alternator is working, the only other possibility is that something is staying on when the ignition is off. Not all new alternators are perfect, sometimes they come with a faulty component that can drain the battery. Also, older batteries can slowly drain if the plates are starting to fail. It's difficult to just give one solution to a problem with so many possibilities.
how do you route the alternator and ac belt on a 2001 Mitsubishi eclipse