A battery that won't hold a charge has a dead cell and must be replaced. This is assuming there is not something on that is pulling power from the battery.
replace it
The sator is bad or you have a short some where.
Rectifier is probably bad. Battery not getting sufficient charge.
Inside the alternator
There is something on that is pulling power from the battery. Any light or any relay that is stuck will drain the battery.
The battery itself could be shot, the lead plates inside do wear out over time.
30 year old battery?? I have never heard of a battery lasting this long. This has to be a record of some sort. I would contact the battery manufacture as they may want this battery and give you a new one for it. Anyway if the battery will not hold a charge it has a dead cell and needs to be replaced.
A new battery doesn't mean a good battery. The new battery may be defective. Return it and get a new new one.
YES
If it will not hold a charge it has a dead cell and must be replaced. If it is just running down overnight disconnect the ground cable in the evening to make sure something is not on pulling power from the battery.
Well, It could be your battery or alternator or both needs to be replaced but it could just be loose or corroded battery cables
try taking your altenater off and taking it to your nearest autoparts store and they can test it . the altenater is what keeps your battery charged i hope i have helped