Does Halfling Luck not trigger when you get a critical failure on what could have been the triggering check? The trigger is "You fail a skill check or saving throw."
I tried reviewing other material to see whether or not "fail" would include a critical failure:
'Warmarch Hobgoblin' includes the language "fail, but not critically fail" which would imply "fail" normally includes a critical failure
but
'Glad-Hand' includes the language "fail or critically fail", which implies otherwise.