Chainsaw Repair

Now we may have a case of chainsaw karma.

I'm not sure what I'm gonna say here helps or hinders the diagnosis, but on a lark I went out and and tried to start the saw this afternoon.  After spraying a bit of starter fluid in the throat, it started right up and ran like a top for several minutes until I shut it off.  Then I started it right back up - ran fine - then shut her down.

BTW, this is exactly what it did last weekend.  When it "died" on Sat., I tried to start it up Sunday morning and it did start.  It ran fine for a half hour or so, then went dead (that "leaning" I described).

Does this  tell us anything?