Well if it continues to run after you shoot starter fluid in it and as HH2 stated, pump running doesn't always equate to injectors injecting, maybe you aren't getting enough current while cranking to activate the injectors.
Once running, the engine RPM is high enough to produce the current needed to both cause and keep the injectors working.
This is purely a logical guess since I know absolutely nothing about Ficht technology. It just seem to make sense to me. Might try a fresh or larger battery. The older carbed Jonnyrudes required the motor to spin around 300 rpm to fire the plugs. I'd guess there is a threshold voltage needed to get the injectors to also work so....
Good luck.