My Sporty was acting up intermittently last year and it turned out to be a bad ingition module (known problem). When the bike was hot it would sometime cut out or feel like it was running on 1 cylinder but, when it cooled down it ran fine.
If your ignition module is located in the same place as mine (right side of engine under the derby cover) remove the cover and you should see the leds on the module flash indicating the ingition is firing. To test it, heat it up with a hair dryer and if the ignition cuts out, its probably bad.
The Harley ignition modules are hard to come by so I replaced mine with their Screaiming Eagle version that was in stock and less money.
Hope this helps,