She needs to not remember the past few years of her life. She remembers who she is and everything else fine, she's just lost a few years somehow.
This condition or injury also needs to be something that surgery can POSSIBLY fix, though it's not a certainty. She doesn't need the surgery to survive (or at least she doesn't need surgery in the near future), and the surgery that could maybe help her memory is also potentially very risky, so her loved ones don't want her to go through with it.
And in fact after she does have the surgery, she still has the amnesia. (This will be modern times and a modern hospital.)
It doesn't matter if it's a brain injury from an accident, or if it's a brain tumor; it just needs to cause amnesia and be potentially fixable with a risky semi-elective surgery.
I've googled and wiki'd amnesia and tumors and the best I can come up with is a low-grade glioma which might do the trick. Does anybody have any ideas?