A...
The original petcock is 24 - 25 years old, and no matter what the mileage on your bike, it is almost certainly dead or it will die very soon at the worst possible time and leave you stranded in a bad neighborhood or dump a tank full of fuel all over your garage. The petcock may or may not be the cause of your current problem, but for your own safety it would be an excellent idea to replace it ASAP. Install a new one and forget about it for another 20 years.
There may be particulate matter (pieces/parts) of the petcock gasket, seals, diaphragm, or vacume line that are getting into the fuel rail from the petcock. It is one source that is an easy fix and like Brian said...forget it for another twenty years. Got mine from 'georgefix' I think or was it bike bandit? Also, if you've never had it out of the tank, there may be a tear in the screen. It is great piece of mind...
(I wouldn.t even bother with the rebuild kits, I bought one and was P.O.'d at the quality and lack of fit)