Battery dies but alternator tested OK?

[jumpsoffrock]

So it seemed my battery was losing juice, so I thought simply I'll start the truck and run it a little which then I'll be ok.

I jump it to start and drive it around the block(15 minutes), once I get back the battery is more dead than before.
Remove alternator and have it tested, it passes test.

Could this problem be caused by the little box that's mounted on the radiator support? How would one go about testing that unit to see if it's bad or good?

Thank you very much.