My theory is:
Because GPIO2 is a Schmitt trigger input it requires 0,8*VDD as High voltage level. That would be 4V in your case. So this design is not really the good. Can you move the input because it is only GPOI2 that has this kind of buffer. If you have a TTL input buffer you get 0.25*VDD+0.8 =2.05 Volts and the problem should go away. Or change the VDD voltage to 3V and run the PIC on the lower voltage.