A ZLC Controller reported two aircraft on approach reported loss of GPS signal.

Narrative

I was working two sectors and cleared Aircraft X on the RNAV approach to SUN and changed them to Tower. HLE Tower called about the GUNKS waypoint and said the aircraft lost their GPS and requested control instructions for the missed. They were unable to execute the missed approach so I issued just a climb to 140. Tower called back moments later to say the aircraft could maintain their own terrain and obstruction avoidance; so I issued 'when able fly heading 190'. I advised Aircraft Y also on approach about the loss of GPS but they elected to continue. Tower called to say Aircraft Y also lost GPS but were able to complete the approach and landing. Aircraft X diverted to TWF and was able to get their GPS approaching the TWF area; but originally requested vector to join the ILS; something not normally done in our airspace due to TWF APPROACH being non-radar. After I had this happen controllers in the area talked and it sounds like this was the ~4th aircraft today affected at SUN and one was affected yesterday at GNG. I wasn't briefed on this at all. Tower put a GPS unreliable notice on the ATIS following these 2 aircraft. If it was a known issue it should've been NOTAMd/noted for broadcast on the ATIS or both prior to these aircraft shooting the approach.Tower was pretty pushy for control instructions from me. It would be nice for them to have a better understanding of our limitations in this circumstance. GPS issues are not uncommon at this airport due to the military nearby. If feasible a conventional approach or at least missed approach would be handy.