いつの間にか + [sentence]
いつの間にか means "before I knew it": a change has already happened, and you did not notice when. It is an adverb and attaches to nothing; it goes at the start of the sentence or just before the part that changed.
The predicate is usually in the past, and very often in きごう〜ていた. That ていた describes the state you found when you noticed – the snow already falling, the wallet already gone – not an action in progress.
Without か, いつのあいだにいつの間に is a question: "when did that happen?", said in surprise. いつの間にか answers nothing; it reports that the moment went unnoticed.