"How do you cope with the same question over and over?"
Drinking.
Ha ha ha ha ha. ;)
Okay, now that I got that over with, I'd say this: I think at this age, a lot of time they are practicing conversation. (It can't be conspiracy, right? :) They ALL do it. And they get stuck on topics. My son is six and once he gets stuck on something, he can come up with about five different ways to rephrase the same subject.
I'll tell you what a wise teacher told me: ignore it. I call it 'actively ignoring' ... at this age, this is what happens:
Child thinks "I say 'isn't that the cutest caterpillar you ever saw?' and mommy will answer me." You answer the first time, the second time, then the third time. Kids kinda get stuck on success, that's why they do the same bad things we laughed at on accident over and over again. (Apparently mine was spitting out green beans repeatedly because Grandpa laughed about it once.) It extends to their interactions with their parents... she says something, you respond, it makes her feel good. And so she does it again, and again...
And it drives us crazy. Something that can help is telling her "all done talking about the caterpillar." and then refocus, but also ignore her when she repeats that question. You told her you were all done answering. You do this calmly, don't remind her too often that 'we're all done with the caterpillar"... I would try rejoining her conversation when she talks about something else.
Remember too that when you feel like you are starting to go bonkers, it's okay to take a break. Tell her you are going potty, then go in the bathroom by yourself and lock the door or something. Seriously. Doris Day is right, by the way, in that you will be helped if you assert yourself and don't feel hectored. If my son were repeating himself over and over after I asked him to stop while we were doing a puzzle at that age, I'd likely say "I'm going to take a break and go (do a chore, usually), I'll come back later". I think it's okay for parents to physically excuse yourself if they are being nagged repeatedly with the same question over and over.