2007 Street Glide shuts off between 4 - 10 miles into ride. Will start back up after a few seconds and run fine. Dealer unable to find any cause.

I believe there was a recall on the 2007 for exactly that problem (something to do with the clips breaking on the fuel line causing that exact problem).
Good luck!

I may be wrong but it sounds alot like a fuel tank venting problem,this may be blocked or not letting enough air into the tank to replace the fuel you have used,this causes a vacuum and the fuel cant flow from the tank to the carbs,after you stop the suction will stop ,letting the fuel flow back to the carbs,check this and see how you go,(i had similar problem on my katana,i just popped the gas cap and problem went away) i later found the vent to be blocked....hope this helps