Car stops running after about 20 minutes

First thing I'd say is find an independent Jag expert and stick by him if the dealer doesn't give you satisfaction. I'm partial to independents, myself, they don't make any money if they can't fix cars.. I'd be checking the ignition system for spark when it dies and since yo say it loses power before shutting down, I'd check the fuel pressure with a test gauge attached and see what happens when it stalls. This should not be hard to diagnose for an experienced technician! Some things to remember: You have an expensive, complicated to the 9's, high performance, luxury English car and it costs money to own one of such. You are very fortunate to have one of my personal favorites (as a mechanic and as a driver) and you can get your money's worth with a committed, experienced Jag tech. Go find one.. If you want to find a specialist, here's a directory link for you: https://repairpal.com/jaguar-repair-in-elizabeth-city-north-carolina