did you rev it a bit for the hole time? ive bought a rx8 with fresh rebuilt engine, but not complete finished. at the first start it was running like yours, but engine turned off after around 20 seconds. im not sure if thats normaly happens, or if it is a fault.
I was giving it gas to keep the oil pressure up and make sure everything gets lubricated well. The engine shouldn't stall out, most likely something else going on.
