I owned a Honda CBR1000F (shameful I know) and it had a very similar prob. Took me days of dismantling to finally figure out some prick had swapped the vacuum line around on the fuel tap. (vacuum safety valve) When engine started it was actually sucking or blowing the valve shut and not letting fuel through but when engine was off it would let enough fuel through to run for 30 secs or so.!
Does it have a vacuum valve on the tap?
