Grand Cherokee '94 Alternator Fuse

[CatFan]

Long story short: Left headlights on 4 hours; Jeep still started; ran about ten minutes and 'Check Engine' light came on; voltage guage shows 12 volts and dropping. Pull battery and charge; replace alternator; still no volts. Discover there is a fuse in the Power Distribution Center labeled "Alternator Pwr. 1" and it is blown. Replace it and all is well (although the new alternator has a high whine). Two weeks later, an interior light is left on for five hours but the Jeep starts just fine. Ten minutes of driving later and the check engine light is on again and the volt guage is back to 12 volts and falling. This time the fuse is badly melted on both sides and reads 4.0 ohms.

Before I go out and get another alternator or have it checked or replace this fuse, any hints what might be causing this behavior? Is it related to the draw on the battery? Could it just be a bad alternator (I know these are all re-builds of some kind although this one has a lifetime guarantee)?

Thanks in advance.