UK Car Repair: 1979 MG hesitates/dies, electronic fuel pump, point gap

Question
I have a 1979 MGB with a Weber carb on it (no emissions control) with the intake conversion and a 1974 points distributor.  The car was set up like this when we bought it.  Over the last few weeks the weather has warmed up to the 90's and the car has started to run rough at low speeds as if a plug was fouling after 45-60 of driving.  The car always runs fine for the first 45 min. of driving.  I have replaced the plugs, cap, rotor, points etc.  Checked the timing, reinstalled points, changed the point gap down to 13 and the tighter gap appeared to help a little.  I also opened the slow idle and it helped a little but the problem still haunts me after 45-60 min of driving.  
We have owned the car 4 years and have adjusted the valves and just completed another tune up but can't seem to find the problem.. but would it be as much fun if it all worked fine?  ;)
Do you think the aftermarket electronic fuel pump could be in need of replacement or ?  Thanks for the advice!

Answer
Hi Rick,
You did not say it runs poorly at driving RPM after the 45-60 min of running so I assume that is OK?
compression fire & fuel is all an engine needs to run so,

1. unlikely ignition related as ign. usually has most difficult time under acceleration and high RPM and high loads. Not what you have.

2. compression can cause a problem at low RPM after hot but easily tested. Pull a compression test (throttle open all plugs out) when cold. drive for the 60 min and quickly pull another test (throttle open & all plugs out) If there is any low cylinder it will show up then. Look up PSI spec but above 135 PSI is OK on that car. 100 or below just about will not run.

3. Fuel related is the most likely. Fuel presure after hot is a possible. Low fuel supply or pressure can cause your problem but if that were true you could not accelerate hard for any distance after the 60 min as that is most demand on fuel supply. But, an overly rich mixture can cause your problem. Here is how to test. At idle cold, slowly and steadily close off or restrict the air supply through the air filter by hand until you see an engine RPM change. Note the responce then drive the 60 min and get the rough idle and do the same test. If it is too rich it will quickly die or run rougher. If it is lean it will speed up a little and smooth out a lot.
Let me know,
HMF