Pilots on commercial airliners undergo regular health checks and wouldn't be allowed to fly if they fail the health check. I don't know what medical conditions would make them fail, you'd have to research whether he'd be allowed to fly with that particular illness (there must be a published list of the rules somewhere). If he's flying is own private plane it might be different but I'd be very worried if there wasn't some kind of checking system in place, similar to how certain medical conditions mean you have to hand in your driving license.
I agree that cancer fits the bill for your description though as I said you'd need to check the medical regulations for pilots.
Regarding being mobile and seeming healthy, the cancer itself may not prevent him from doing various things until close to the end but the treatment (chemo, etc) can be very debilitating. The chemo drugs may prohibit him from flying planes (very strict rules about what pilots can and can't take and still fly a plane). You'd have to fit in phases of undergoing chemo in between when he has to do physical action stuff, fly planes etc.
I think the organ transplant scenario (as suggested above) would fit your story better. He would be very fit and active but still need to take the anti-rejection drugs and various other drugs, but would risk suddenly getting very ill and dying from an infection, as the anti-rejection drugs suppress the immune system. Antibiotics would take care of most bacterial infections but a bad viral infection or an antibiotic-resistant bacteria could kill him. My 2nd cousin had organ transplants and died of flu. People who've had donor organs can't have vaccines and rely on herd immunity and staying away from ill people. In the UK their family would get free flu vaccines on the NHS in order to protect them.
I can't really comment on whether any of the above treatments would be expensive enough for your story as they'd all be paid for on the NHS in Britain, though I'm pretty sure cancer treatment would be. As long as your story's not set in Britain that's not an issue, though I think you'd need to have a reason why the insurance company doesn't fund it (not sure how this works to be honest, so maybe it's easy to find a reason).