One other possibility. I had a 009 that was in good shape, but would not run. I could see fire on the plug just fine, but finally decided that perhaps it was weak. I put a new ignition module on it and it cranked on the first pull. It absolutely would not hit a lick before.
Seems like even if it's flooding it would hit a time or two.
It's also possible, especially on the 009 but possibly on other saws that the sparkplug wire is going bad, when you turn it one way it fires, when you twist it the other way it doesn't. It happened to me on my 011, bout' drove me crazy finding it. You can try pulling on the starter when the lights are out to see if you see an arcing of the spark at an unwanted place.