How can I repair a bathtub that is peeling?
A picture would be handy, but I am betting the tub was refinished in place with a spray on epoxy at the most or a harry homeowner kit at the least. Either way the warranty for both surfaces is limited. It may be able to resurface it again, but you see what the product will look like in a few years if it is possible to redo.

The most reliable way to solve the problem is to replace the tub. Or..... you might want to hire a tub reliner company, which will have limited life as well, in my opinion. I would do the replacement tub, not the "refitter"