Car dies after an hour!

As the title says, my car has been dying after about an hour of stop and go driving in warm weather. It always happens when I come to a stop and suddenly the idle will drop to around 600rpm and if I try and give it gas I can keep it running for a second, but eventually it will just die out no matter how far I push down the pedal. Once this happens, I attempt to start it by turning the key and pumping the gas pedal. Finally, after about a minute of cranking it over in traffic it will fire up and as long as I keep the rpms above 1500 I can get it home and out of the street. I have had this problem for as long as I can remember, and I have just been avoiding driving the car for too long. I have replaced the TFI module (about 6 months ago), distributor (after the stator went out), coil, fuel pump, fuel filter and pretty much every other sensor in the time I have owned the car. My thoughts still lean towards the TFI because this occurs when the car gets warm, however I have already replaced it twice. I plan on having the TFI checked tomorrow, but I need some ideas on what else could be causing this. If it happens to be the TFI, why would it go out so soon? Please help!!!

the supplied grease was applied when I installed the module... I will get it tested as soon as possible. As I was brainstorming on the situation I realized that this problem started ever since my alternator caught fire and the fusible link that leads to the starter solenoid melted. I replaced the link and rewired the alternator using 6 guage wire and I'm wondering if its possible that the fusible link i replaced it with might be too short. I figure if this heats up it can prevent proper voltage from reaching my computer and ultimately stalling the car. Any thoughts on this?

TFI tested ok after three tests(to heat up). I looked into a fuel pressure guage but they want 50 bucks for one so I figured I might as well buy one I can put on there permenately. Even though I have a new pump, bad fuel pressure is the only thing left I can think of.

I do not have an aftermarket ignition... and I agree that it might be something electrical due to the effects of heat on old connections/relays. On thursday I plan on installing a stage 1 cam, and along with it I am going to get an adjustable regulator a fuel pressure guage. When I pull it apart I'll be able to check all my connections thouroughly and maybe I will run across something.