I know nothing about the carbsetup on your engine, but...
FUEL;
If there is a blockage in the fuel ine, it could be slowly starved of fuel,
If the diaphram in the fuel pump has gone, it will starve it of fuel,
If the float height is wrong, the car may 'run out' of fuel,
If the fuel filter is blocked and dirty ...
If there is no fuel filter, then the jets in the carb may be full of poo.
Electical
Coil failing after it gets warm,
Plugs = doubt it
Cap & arm = nope
Little plug on dizzy, maybe, but it would be more inconsistant
Ign barrel = see above
It may be something simple like that or... I dunno.
Let me know if you are unsure on how to test the above.
Cheers
kraM