Bad connections along your ECU. Check your wires leading to the ECU. If all is good, you might look into getting your ECU reprogrammed.
p.s. If the wiring job on the swap looks like crap, then your ECU is probably
fried. This would make sense for the reason it acts up once you drive for sometime, your ECU is overheating.
When I had my civic, I had some wireing issues with my swap, it would sputter and die for no reason and wouldn't start back up for an hour or two. Once I had a professional redo the wiring it ran fine.