Harley-Davidsons all have their quirks and one of them is that occasionaly they will stop running for no apparent reason.  Strangely, the most common reason is that they have run out of gas and the owner doesn't think to turn the petcock to reserve because they see plenty of gas in the tank.  I always check my new bikes reserve by intentionally running them out of gas until they hit reserve so I can see exactly how much fuel I can count on.  Reserves can vary however and there may be as much as a gallon and a half left so the first thing to try is turning the reserve on and waiting a minute for the carb to fill. 

 

If that doesn't work there are a couple of things I'd check, two relating to fuel and the other relating to ignition.  I guess the question I have is that when it cuts out do the lights stay on and does the engine crank?  Since I don't know I'll give you the fuel and ignition problems we see pretty often. 

 

Out here in AZ we have vapor lock and venting problems on many bikes and both have the same symptoms.  The bike just runs out of fuel due to vacuum in the tank not allowing the fuel to be fed by gravity to the carb, or fuel doesn't get to the carb due to gas boiling in the fuel line.  Both can be cured easily by modifying the venting on the right side gas cap.  Unscrew the cap and look at the center inside.  There is a spring loaded one way valve in the middle and it can malfunction by either not letting air in freely causing the vacuum, or it can seal up and not let the expanded vapor out causing pressure and flooding the bike.  Use a small (1/16" or less) drill to add a small vent hole by drilling one of the 4 plastic flat spots that encircle the center valve.  Be careful not to drill clear through the outer cap.  When you are done it will allow pressure to bleed off or air to enter to prevent vacuum. 

 

The other thing to check in the fuel system is the vacuum petcock.  Make sure the vacuum hose is connected to the manifold.  This vacuum hose is what opens the petcock and if it loses vacuum the bike will run out of gas.  Sometimes things that share the vacuum like Kuryakyn Hyperchargers can affect it also.  Check the petcock by disconnecting the fuel line.  There should be no gas flow.  Crank the bike over and the vacuum should open the petcock and let the gas run out.  If that works it's OK.

 

The next thing to check is pretty common in the electrical system.  It involves the charging system and specifically how the wire from the voltpak is connected to the main circuit breaker off the battery.  The factory connects it on the side of the 30Amp breaker away from the battery.  This means the breaker kicks out if the voltpak shorts out or if there is too much draw on the system.  It also means that if the battery gets too low from sitting the charging system can try to push a lot of current through the breaker into the battery and kick the breaker out.   Since it is a thermal reset breaker it makes a "tink" sound when it kicks back in and then everything works again.  The charging output is RPM dependant so the bike might run longer if you are riding slowly.  Find the 30 Amp breaker, identify the charging wire (usually a thicker rubbery type wire) and switch it to the battery side of the breaker.  This usually cures the problem.  An alternative to this is to keep your bike on a suitable trickle charger like the Deltran Battery Tender so it will always be fully charged and the charging system won't have to play catch up.  An additional benefit of this is that your battery will be protected in case of a voltpak or voltpak wire shorting out.