If there's a medical reason, AA has been quite accommodating IME.
Case 1: A few weeks ago, we were sending my stepson out west to spend the summer with his dad. I used miles. Had the flight booked for a Saturday (and he was in F too, so quite happy
). Monday, his dad calls and tell us his grandfather died, and he'd really like him to be at the funeral. Funeral's Saturday morning, and he won't make it in time. My wife called AA, explained the situation and gave them the funeral info. AA waived all fees and put him on a Friday flight. Just had to pay a difference in miles to use an anytime economy award. Only problem was they forgot to recollect the tax on the new ticket (refunded original), so it wasn't issued until later on. Easy fix though.
Case 2: Was heading on a trip to ICN in paid F (non-refundable). Had already checked in for the trip the next day. I was over by BWI heading to the office to pick up a laptop and I got t-boned by a bus. Needless to say, with several broken bones and other injuries, I wasn't taking my flight the next day. Wife called AA and they canceled the ticket and waived all penalties and change fees. Used the credit later on when I made the trip.
YMMV, of course. However, I've found if you have a legit case, and can back it up if requested, that they'll work with you.