Alternator parasitic draw?
Also if you jump the thing and let the alternator charge the battery it will die if it's idling, rev it some and something smells like melting plastic. Swap the alt and move on?
The melting plastic smell is (likely) either a malfunctioning alternator regulator (plastic rectangle on the back of the alternator), or the fusible links heating up while trying to charge a dead battery. My '94 F250 has two grey forty amp fuse-links in parallel on the alternator charge wire. They connect at the fender solenoid where the positive battery cable bolts to the same solenoid. Charging a dead battery with the alternator is hard on everything.
Batteries can short out internally and drain themselves. It's uncommon, but not rare where they'll charge up and act normal for a while, but if they sit they will die.
If you replace the alternator make sure you charge the battery all the way with a charger or take it to Wal-Mart or a parts store and they'll charge it for you. They can also test it if you're at all uncertain of the battery's condition. If you take in your alternator or get a junkyard alternator the parts places can test it too. That way you eliminate these components as problems if an electrical malfunction persists.
Also - Please don't take these basic instructions as an insult. I don't know if you know this stuff or not. I often take for granted that not everyone has a multi-meter and battery charger and knows how to use them, so I err on the side of caution and say a lot of simple stuff. Don't get overwhelmed either - the charging system on these trucks is relatively simple and the factory wiring is stout.



