Possible fuel starvation due to vacuum in the gas tank. When the vents (in the fuel cap) stick shut, either pressure or vacuum will build in the tank. It it's vacuum, it will eventually prevent the fuel from flowing. When you stop for a bit, enough air will leak into the tank to allow the fuel to flow again, but not for long.
A fix is to remove the small orange diaphragms in those vents.
Of course, it could be something else entirely...
Life is a mortal adventure. Don't avoid all the risks.
2005 KLR650, ready for the world
1999 KLR650, badly in need of TLC...
1998 Honda Valkyrie Tourer
2001 DRZ400e, already broken... in