I am not a lawyer but this is just my read of The 25th Amendment.(Assuming normal times in which the president doesn’t command a vast cult) The 25th would probably be exercised since the president would be unable to perform his duties and discharge orders, so the Vice President would wield presidential powers without getting the title proper; this has happened before when the Prez has underwent anesthesia for routine medical procedures, but the Prez likely had written out that they would be incapacitated in advance. I don’t see anything that would apply here for the Prez to lose his title before his 4 year term expires since he wouldn’t be declared dead due to the sympathy the Gov and the People would have to rescue him. He would lose his title if the kidnappers allowed him to communicate that he is unable to fulfill his duties and discharge orders, but this might not be considered invalid since it was conveyed under duress and would limit the push to rescue him.

I assume I’m talking to either Nicolas Cage or Melakon?