If it's an older unit sometimes a worn idler bracket mounting allows the assembly to flop around and get the idler pulley out of alignment with the end result being a thrown belt.
By drive belt you mean the one that goes to the transmission correct. And the large pulley would be the one on the tranny. If so check the support bracket bolts toward the front of the tranny. If they come out will allow the transmission to rock and throw the belt off.
If it's an older unit sometimes a worn idler bracket mounting allows the assembly to flop around and get the idler pulley out of alignment with the end result being a thrown belt.