Have you played with the mixture? It sounds to me like it's leaning out. That could also come because your carbs are too worn and they're leaking more as they heat up and expand. If you were really getting vapor lock, giving it gas wouldn't change anything. It would still die.
Once it's warmed up, try spraying a little carb cleaner around the ends of the carb shafts. If the engine slows, they're leaking around the shafts, and the carbs need to be rebushed.
Philippe
'57 MGA "MILOU"
'66 MGB-GT "TINTIN"