Hall Effect Shielding
You should not have a 0.1uF capacitor on the amplifier output. Remove that and it may magically start working again. From the datasheet: 


  AD626 is stable driving capacitive loads up to 50 pF
  (G10) or 200 pF (G100).


So it's probably oscillating, which can manifest itself in strange behavior such as apparent large DC drift with temperature or time.