Is there data on this? Specifically I wonder if women who refused it for a first birth still refuse them for subsequent births (or maybe they change their mind?).

I don't have any good data and would also be interested. Anecdotally, I do know women who didn't use them at first and started using them later for multiple reasons: aging, advice of medical team changing, unexpectedly low pain tolerance, and in a couple of cases, just wanting to experience an epidural with the last kid. :)

I also know some who stopped using epidurals, but fewer and most of them simply had become interested in more natural births between children.