I plug/unplug 10+ times a day. Can't imagine normal use would cause damage to the port. It's no cheaper in design than what i've seen in other products. So maybe you were being a little les than gentle with it when it broke? Just sayin' considering we haven't really seen threads complaining about the port's quality.
With others, shouldn't be hard for Sprint to trade you for a charged battery to get your backups done and prep for a replacement. Though not paying could be questionable because they might deem user abuse and not a defect, though I'd give a one time pass on it.