It could be a number of things such as bad gas (water) or even a broken injector wire right near the plug on the injector. They were notorious for that. Do the wire wiggle test when it is running and see if the engine cuts out when you wiggle the injector wires near the plug on the injector, usually within an inch or two of the plug.
You didn't say if the lights go out when this happens but there is also a breaker problem in those year bikes too, it's been upped to a 50 amp from 40.
Could be a engine sensor or even the fuel line inside the tank.
Do you hear a hissing coming from inside the tank when it pressures up? Does the fuel pump recycle the second time if you let it sit a minute?
Do you get any flashing lights in the speedo while running or after startup within seconds indicating a fault code?
Have you checked for spark at the plugs?
Are the plugs wet with gas?
Here's how to check for a code on that bike.
It's difficult or even impossible sometimes to diagnose a problem over the internet without complete information when this happens. Look for more symptoms like explained above and post back again.