Amex entry at JFK is valid for 3 hours. In my experience, if you arrive more than 3 hours prior to your flight time, the staff will warn you that the pay-in fee (for another 3 hours) will apply if you do not check out with staff and depart within three hours of your arrival to the lounge. I don't know how carefully they track and enforce this procedure, but I sensed they did at least keep a list of the visitors that were potential "holdovers".