I also have to put my two cents in. DUring my mileage run this year to requl for exec plat, I was flying JFK-LHR-JFK. Connection time was 3 hours (Leave Sat night, Arrive Sun Morn, leave again Sun afternoon, arrive back in NY Sun Afternoon). JFK-LHR delayed by 2-1/2 hours, I make it to LHR 1/2 hour before my flight back. AA staff very helpful (a) trying to get me back on my original flight (they had moved me to the 4pm departure seeing as I would not make the original flight in time) and (b) offering to upgrade me (from J to P) if space permitted (missed by 1 person by J was fine and ended up knowing the FA on the flight).
I even had a nice long conversation with the supervisor for the flight and now have a connection the next time I fly through LHR.
--Jim