No, that doesn't happen to mine, unless I purposely pull it off. I don't use clips with teeth though either.
Try lining the clip with ribbon, width that will fit the alligator clip. Maybe the bow would stick better to the lined clip? Sorry, not sure though.
I use the mini hot glue gun from Walmart and their mini glue sticks. I just wonder if it is your glue?
Sorry, not much help here, maybe someone else can help you!