Wanted to share some good news.
Jetblue wrote back and offered to temporarily return the credit for a 2 week period and allow my father to use it to book tickets for himself or friends and family.
So, this story has a happy ending although I really do wish that Jetblue would update their system so other folks would be able to more easily see the expiration date on their credit and avoid having this situation repeated for other people.
Thanks for everyone's feedback!