Both my VX's had similar problems - sometimes the issue was getting the VX to stay at idle after initially starting, and at other times getting them to stay running after coming to a stop.

Turned out to be the fuel pressure regulator. Roughly a $50 part. Not sure if that's the issue you're facing, but you might wanna have a mechanic check it out... After mine were swapped out I've had no issues at all.

-biju.