IPhone5 hot spot stops working while charging?

I have an iPhone 5 i purchased in February 2013. When using it as a hot spot, it works perfectly as long as it is unplugged… (i can run my ipad and HP laptop PC from it). The problem is when i plug the iPhone in to charge (since the hotspot drains the battery so quick), the hot spot stops working IMMEDIATELY after i plug it in. I've contacted AT&T and the apple store, nobody has been able to figure this out yet. This has been a problem from the first day I've had it, so any help or suggestions you may have are appreciated.

Turn it on again.