Check your engine mounting bolts! I almost totally ruined a Poulan 2900 by using it so long with loose and some missing bolts - they ruined the mounting holes in the engine block and I had to re-tap for new bolts. Some of the symptoms I was seeing included the chain being thrown (even with new bar and chain), along with the mysterious changes in chain tension. The engine movement also pretty much ate up the inside of the plastic sprocket cover. I felt pretty stupid when I finally discovered that all the problems were simply due to my own stupidity and poor maintenance!
In fact, I was just putting on a new rim sprocket and dressing the bar on that same saw today, and while I was testing it for good oiling, I ran into the same problem with magically tightening chain. Sometimes it goes suddenly very loose, and other times it goes super tight, all for no obvious reason. Flipped the saw over and found one of the mounting bolts almost out, and another two less than fully tight! Even after the first re-tightening, they started loosening up again VERY quickly - finally had to bear down on those bolts harder than I wanted to stop that game.