The song requested repeatedly can mean something different to the person required to sing it.

A request is an act of affection from one side and a piece of work from the other. The people asking are returning to something that moved them, while the performer has done it four hundred times and may be reaching for a feeling that left years ago. Both are sincere. Only one of them is being asked to produce the emotion on demand.

If you ask someone for their signature thing, accept a no gracefully. And when you are the one being asked, you are allowed to say that tonight you would rather play something else. Willingness is part of what makes it worth hearing.