Old batteries that have been dead a few times are trash.
Make sure that the trunk light and glove compartment lights turn off.
Best have the car electrical's checked before the new battery goes dead.
An bad alternator sometimes drains the battery overnight.
Lead acid car batteries are damaged by being dead, not like lap top batteries.
Time for a new battery.
Chances are the alternator is OK because it put some change back in the battery in the 20 min drive. The battery is just weak and not holding it properly.
Classic signs of a dud battery.
Like a dog it should only be allowed one bite. It lets you down get rid of it.
Sounds like a bad battery. Here is how to test it to see if it is bad:
NEW battery,.....cheapest & easiest fix
My battery died over the weekend, previous to this it had all been working fine. I had it jump started and it got going again, I drove it around for half an hour to get the charge going before turning it off. I went back 20 minutes later just to check and it started fine again. However, I have gone back to it today and again it is failing to start, making the clicking sound it did last time without turning over. Is this a case of a new battery needed, or could it be the alternator. The car was purchased only 3 months ago and I have no idea how old the battery is (10 year old car), but from looking at it I can assume it is fairly old.