IPA: /ʌnˈfeɪlɪŋli/
KK: /ʌnˈfeɪlɪŋli/
In a way that is always reliable and consistent; without fail.
She unfailingly arrives on time for every meeting.
Unfailingly → It is formed from "un-" (meaning not) and "failing" (from the root "fail" which comes from Old French *faillir*, meaning to fall short or to be lacking). The word means not falling short or lacking, thus indicating reliability or consistency.
Think of 'not' ('un-') falling short ('failing') — that's why 'unfailingly' means consistently reliable.