My 1125r had this same issue. It would start then die after the RPM came back to low idol. You had to massage the throttle until warm. I ended up burning out my fuel pump and haven't had this problem since....
Either way, they're notorious for having issues with the cold start. Make sure your have quality fuel and the bike is breathing correctly...
lamarchangel is right, do you blip the throttle a lot - 1125 does not like spikes in throttle and tends to shut off when you do this, at least until you take out AIS and adapt yourself to Rotax's power curve which is finicky when it comes to of the line acceleration in comparison to XB platform.
Two things to do:
1. Remove active intake solenoid and install resistor plug from the delaer ( dealer might try to tell you it crucial to the bike operation, however it only there to get bike through the noise test ) (and to mess with your idle and blips)
2. Is this your first season on it, why? well if you came from XB platform, power curve is different on the Rotax and does require to be revved a little higher. I had problem with this when I just switched. If you are trying to ride around town at 2k it ain't gonna happen - redline is at 10500rpms so don't be afraid to use those rpms and run at minimum of 4k.
