And no. You lie again, she never burned anything.
and it was only 2 times and none because she exhausted permanent powers because that has never happened (not even with the AoA version).
1) when by a strange energy both she and Gambit were depowered for a time, and nothing had to do with burning them and 2) when hope and she came into contact in Messiacomplex it caused a short circuit, but Rogue did not have control of her powers and Hope had that resonance with Pforce, and Rogue only lost sunfire's powers, not absorptive ones, and it had nothing to do with depleting them either. In fact there are two future versions of Rogue and both have multiple powers and control of their absorption powers, so they could also already master the recanalization of past powers.