The most common cause for the heated seat shutting off after a short period of time is the failure of the seat element. The seat element is the most common cause and can be verified by testing the resistance of the element. High resistance or an open would cause it to shut off. I have a 2010 raptor in the shop with the same issue, ordered a drivers seat heat element(open). element should be between 1.6-2.0 ohms let me know if you have a multi meter so we can test. At the dealer we would start with checking the HVAC for trouble codes.
lets start here
I am looking for the part#. the procedure says to replace the cushion with the element. I have done just the element at this dealer. The key is to pull slow so the foam cushion does not tear. The new element sticks to the foam cushion like a band aid.
I have done a bunch under warranty, never asked how much.
searched on a parts site and found it for 50$