Miata Engine Problems - 2002 Mazda Miata

My 2002 Miata has an intermittent fuel pressure problem usually on a hot day after running well for hours. Symptoms are hesitation, bucking, missing or stumbling. No CEL is on or stored. After it sets for 30 ? 60 minutes it usually runs well again at least for a while. I replaced the CAS, CPS and EGI Main relay. I ran with a fuel pressure sensor for a while and found that when the problem occurred pressure was erratic. At the time of the failure turning on the key resulted in no pressure at all. So I had the fuel pump replaced.

I ran the car for a couple of hours on Saturday in 85+ temps and it seemed fine. However, after taking a 15 ? 20 minute break at a park it would not start. It exhibited the same problem again though the pressure sensor had already been removed. I guess the fuel pump relay is next. What else could cause this?