Any electrical cct / system is only as serviceable as the last time it was used or tested. Testing is c/o on FFOD & on preflts etc.So could be tested many times daily.Probably enough without continuous monitoring.
As stated a fault will not necessarily preclude the loop giving a fire warning.
Unless being used because of a DDG item the apu generally used on or close to the ground.
Been working 737's for many years with very few APU loop failures.I've not personally seen or been involved with a 737 apu fire.
Ideally everything would be full time monitored but it aint a perfect world and neither is full time monitoring.