sounds like you might have a clogged float valve. it's not feeding fuel to the bowl fast enough so your bike will run for a few seconds till the bowl is drained, then cuts off till it can slowly fill back up.
try checking that, if not then it's gotta be a leak somewhere, once you get her fired up, spray some carb cleaner around the boot, carb, etc and see if the engine speed changes.
it could also be a jetting issue.