This is the adverb of 'unfailing': it means always, every single time, without ever once slipping — and it usually carries a note of quiet admiration for someone who kept it up when it was hard. Its main job is to sit in front of an adjective describing a person: unfailingly polite, unfailingly kind, unfailingly cheerful, unfailingly patient, unfailingly generous, unfailingly courteous. That pattern — 'unfailingly + nice adjective' — is where you will meet it almost every time. It can also modify a verb ('she unfailingly remembers everyone's birthday'), though that is less common and sounds a little formal. Compare it with 'always'. 'She is always polite' just reports a fact. 'She is unfailingly polite' adds that there were chances to be otherwise and she never took one; it praises the person for holding steady. That extra layer is the reason the word exists at all. Register: formal and warm — references, tributes, thank-you speeches, book reviews, obituaries. In casual conversation you would say 'she's polite to everyone, no matter what.' There is one small mischief worth knowing: because it sounds so complimentary, English writers sometimes use it drily, to praise something faintly or with a raised eyebrow — 'the food was unfailingly beige'. You will only catch that from the surrounding sentence, and A2 students are not expected to. But it exists, and now you know.

始終、無一例外地（後面多接正面形容詞，如 unfailingly polite 一貫地有禮）。比 always 多了一層「明明可以破功卻沒有」的讚許意味。