Try to prove what it's losing.
Sometimes if you can't find the cause of something like this, or the failed part, you have to come from the opposite mindset....sort of diagnosing backward.
So to start off, is it losing fuel or spark?
If it fires right back up, you know it's not spark (at least it's a real good indication that it's not spark).
If it only does the problem once it's warmed up, you know it's not spark (again....or at least it's a good indication that it's not spark related).
When you write in for help, take extra time to be very clear about the description. Use words and phrases/sentences that convey exactly what's going on. It helps others help you faster, and more accurately.
For example, here's what would be better....
It runs fine when cold, but once up to operating temurature, it'll die unless I give it gas when stopped for a traffic light or stop sign. It accelerates fine, and is fine and normal running down the road.
Anyway, back to your issue.
Let's say that it's a fueling issue. That can mean 2 things a) it's not getting enough fuel b) it's getting too much air
So if we're pursuing this line of thinking, what controls the amount of fuel that the engine gets at idle? More importanly, what controls the amount of fuel that the engine gets once it's warmed up? Engine coolant temp sensor that feeds the computer, the wiring from that sensor to the computer, the Oxygen Sensor, it's wiring, the TPS and its wiring, the fuel pump, the fuel filter.......etc.
Same thinking process for what controls the amount of air getting into the engine, and in this case, you also think about what's attached to the intake manifold that can leak air into the engine. EGR valve, IAC, Brake Vacuum Booster, Dash vent controls, transmission controls, PCV valve, etc.
My suggestion would be to set the ignition timing to factory spec, hook up the timing wire, and then pursue the issue. You may have a failed computer, and that's why, when the timing wire is hooked up, the engine runs so bad. I'd certainly get on ebay and buy a computer for it and use it to test and rule out, or cure the problem. Same with the oxygen sensor if it's not been replaced, or the new one is some cheap China junk