Mary,
There are a few possibilities. First, do you have the updated injectors? Mid way through '06, Harley Davidson changed the injectors from 8 degree to 25 degrees. You should be able to find this out through you local dealership. If you don't they will replace them as per Service Bulletin M-1185, free of charge. If you do have these injectors, the next question for you is, do you have a PowerCard on your bike or not? If you don't, then youlikely have a lean condition that could be causing the bike to stall. If you do have a Powercard on your bike then your green fuel may be turned up too high which is causing a rich condition that can also stall the bike.