The DX6i uses 4 AA batteries as well, but comes with rechargeable AA cells. You can do the same thing, get a set of rechargables with a a charger so you can top them up before going out to fly. I have been using the AAs for a year now with hundreds of flights and it has been rock solid. The DX5 is a decent radio, I bought one for my daughter so we could buddy box.
I really think your problem is the ESC, read the links Chellie posted, a seperate UBEC can be used with the E-Flite ESC.