GFCI turns off with bath light
Somehow the wiring has gotten mixed up.  That receptacle is now being switched along with the bathroom light. The receptacle needs full time power ahead of this switch. However, this receptacle should not even be on the same circuit as these lights.  The receptacle should be on a 20-Amp circuit, 12-guage wire.  Bathroom lighting is usually on a 15-Amp circuit, 14-guage wire. Hair blow dryers, use in bath rooms require too much power for a 15-Amp circuit.  Hope this helps some. P.