“I’m fine” in a flat voice is a sentence worth a follow-up question.

The words are a door being politely closed, and the tone is the part telling you the room behind it is not empty. Most people will not volunteer more on the first ask, partly to see whether you were really asking. A second question is how they find out, and it costs you about four seconds.

Ask again once, more quietly and differently: are you actually fine, or fine fine. Then stop. If the answer is still fine, believe it and stay around. Somebody who knows you will ask twice tends to come back later, when they are ready to say it.