I looked through posts to find out if there was any other person who had this problem with their bike and couldn't find one so here goes.
First of all there is no pattern to the way the bike behaves.   I have ridden over 100 miles before it back fired and then chugged to a stop and I have ridden about 40 before it did the same thing.  After I sit for a while, maybe 15 minutes it starts up and runs fine till it does it again.  The last time it happened I went about 40 miles before it stopped, got it started and went about 10 and it started and then about 1 city block.  At that point I had it towed home.  

I is a 2009 S40, has about 23,000 miles on it, a 2 year old battery and it had a fresh tank of gas last time I rode it before I had it towed home.  I am in the habit of putting gas additive in the tank when I fill it.

I have since taken it to a mechanic who has had it for over 3 weeks and he seems to have no clue but thinks it might be electrical.  I changed the oil about 1000 miles ago.

Any ideas would be appreciated.

Thank you so much.  I'll take this to the mechanic and go from there.

test the petcock, look it up in the tech section index.

OOps, i meant reference post "Bike acting bad, then dead, no electrical power"

Chances are it's the stock petcock, I'd be willing to bet that each time it failed and the bike died you where riding at highway speeds .At those speeds the butterfly of the carb is  open wider and the vacuum in the carb is lower,the spring in the carb closes the diaphragm cutting off fuel flow to the carb bowl because there isn't enough vacuum to fight the spring pressure .If I'm correct, you need a Raptor petcock.

Thanks for all the input.  So if the mechanic isn't the best place to take the bike for electrical problem what does one do?  I know how to change the oil. lol  That is it.  And, the mechanic has not found the problem.  I took the bike home, rode it 5 miles, it backfired, stopped and wouldn't stay lit so he came and got me and the bike and it i back in the shop.  He checked the petcock and said it was ok.  I printed off the other suggestions and he tried various ideas.  Does anyone want a 2009 S40, black, side bags, wind screen, back rest?  

He checked gas flow and we were lucky because it "behaved" exactly as I hoped it would when he came to pick it up.  I am in Springfield Ohio for now.

Just kidding. I love the bike, it is a lot of fun to ride and I preferred it to the 800 Intruder I gave to my son.

How long did he let it idle ,until it overheated? I hope it wasn't sit on the sidestand ! did he check the petcock ?or the fuel level in the carb bowl after it quit? Almost sounds like he's to busy working on other bike to fix yours.