When it shuts off, take the can of starting fluid out of your pocket (hint, hint) and spray it into the air cleaner.
If the bike fires: It's fuel related. Likely a pinched line or blocked up internal tank, fuel screen.
If the bike doesn't: It's electrical. Could be a faulty (when hot) cam sensor, or even an ignition switch with worn internal contacts.
“When the going gets weird, the weird turn professional....” ~ Hunter S. Thompson~
R.I.P. Rubberdown. 1971-2012
2005 E.G. Classic
Baisley Oil spring
Rinehart 3.5" pipes
S&S adj pushrods
3 stickers, adding 5 hp each. I swear......