I have a 600 and I had similar problems. After riding for a while it would stall out on me and I would have to let it sit for a while, then it would start back up.
I drained the tank, cleaned the hardlines, the vent tube, put in some new NGK plugs, changed the oil/ filter, cleaned the air filter, put in some fresh 91 gas + some carb cleaner in there and that pretty much did the trick for me, runs smooth, idles well.
so you might wanna check out all of the routine maintenance stuff before you take it to a shop to get checked for a ton of $.