Healing a warrior in Brayflox who won't put up defiance is a nightmare. The mobs hit relatively hard and your health will be extremely spiky. If you are dying then what you are doing is a dps loss and defeats the purpose of dropping defiance. The healer was probably sleeping mobs because they literally could not you up otherwise. OP, your healer was a saint if they completed the dungeon with you anyway. I would have vote dismissed you if you had not put up defiance after requesting you to.

That said, there are times you can drop defiance to push dps, but this should be after establishing solid threat, after your healer has a good handle on your health, and with a major defensive CD up. Learning to stand dance isn't a bad idea but if you happen to die when defiance is down this is always your fault.