I think ProF is absolutely right on this. I think the carberated bikes are gravity fed from the tank, and that there is NO fuel pump. My mistake. See here:
Fuel System Troubleshooting - Harley Davidson Community
However, from your description, it still seems like a fuel problem, although we should eliminate NO SPARK problem. So the next time the bike quits like this, pull over, jump off and pull the wires off the plugs. Make sure the bike is in neutral, and crank it over holding each wire to a good ground (not the spark plug, and definitely nothing that has fuel in it!!) and look for spark. Might have to put something metal (like a 1/4-20 bolt) in the plug end of the wire to see the spark clearly. If both wires are sparking - GREAT!!
So if it is NOT spark, then back to fuel problems. Get a small flashlight and your eyeball in your tank and look towards the fuel port as much as possible. Is there a bunch of crap in the tank including water?
Close the valve on the tank and get another hose to drain the gas from the tank. Collect about a pint in a glass jar. Hows it look?
Drain the tank and take off the valve and strainer. How does that look? Clean everything up, or replace the strainer if possible and reinstall.
If you have the Keihin CV carb (if not, skip all this), drain some of the fuel from the float bowl into your glass jar. (See here:
Poor Performance With Carb Models - Harley Davidson Community) How does that look? Here is some good stuff on those carbs:
Keihin (CV) Carburetor Info - Harley Davidson Community
*Twin Cam CV Carb Rejet Suggestions - Harley Davidson Community
If none of this has helped, let us know and we will go back to the drawing board (self-help section).
TQ