??? I have a '93 that has very similar stalling issues to others that have posted...
They began in Sept.2003. It was a dark & stormy night... rpm started to go down and no amout of throttle would get them up- seemed to kill it actually.  Waited 10 min or so,, fired up again,  5 min riding...putt,putt cough, dies. Same thing. This repeated through rush hour traffic for an hour, each time getting about  .75 mile each time.  
I thought because of rain, it could be electrical. At that time did not think of fuel petc**k, but sure felt like a 'compression issue' to a rookie.

Called mechanic for tow and swore I'd never sit on her again.
$400 later, could not afford another ride, so kept it...
Ran GREAT all summer 2004 through cold rainy spring too & hot dry days!, until one fateful dark & stormy September night in rush hour traffic....

Deja vu...I could not believe it. Same thing. This time I called a friend with a trailer, saved $400 and still don't know what the heck it is.

I have limited knowledge, a bit more confidence and enough mechanical aptitude to try anything once.  

First thought it was Fuel Delivery- off came the Fuel Petco*k, hoses, carb. all 'looked' OK- gas cap off made no difference  but did notice that while gas 'ran' out of the hose on PRI, it kind 'dribbled' on 'ON'. The diaphragm looked a little 'lopsided', but not knowing what a 'good one' looks like, I have no comparison.

Then dicovered a thing called a 'decompression cable' that must be checked- I know I've never done it...

Then I thought it might be a sticky valve- MMO has been praised on other sites.

I am ready to cut the tank in half and use the entire thing as a planter/yard ornament.

Why did it run for ONE YEAR  almost exactly, but die in the exact same conditions, when it had ridden through many crappy days in June & August?

Can anyone tell me what size the vacuum hoses are - I'm at work and gonna stop on the way home to get new ones- start with the basics.,..
I am ready to scream! Waaaay passed the swearing stage!

TIA
Martha

Martha,

I have an '02 and have had similar, but not exact, problems as you describe.  

As you suggest, the first thing I would do is replace the vacuum line from the petcoc- to the carb. Just make sure the clamps make a good seal.

What has also helped my bike is the addition of Marvel Mystery Oil or 2 cycle oil to the fuel. I like MMO, but have used 2 cycle oil. Now, I rarely fill the tank up without adding MMO and from time to time I also add Seafoam.

Much luck with you diagnosis.