TC45DA, TC40DA, Farmall Super A, New Idea spreader, Dolmar and Echo saws, Yanmar MIniEx, Ford 3550 backhoe, lots of junk
If the chains that you have aren't too too bad, you can file off the burrs that have formed on the drive links and are preventing the chain from fitting into the bar. Any chain can come off of the bar under the right (or wrong) conditions. I wouldn't over-think this. Try again. Might just be that you had two bad cutting situations in a row. Might not have another one for a long time.
Which way where you cutting when this happened. Using the bottom of the bar so the saw was being pulled into the log or the top of the bar where the saw is being forced out of the log? I have had problems with newer higher RPM saws throwing the chain when cutting with the top of the bar "pushing" the chain through the log.
This method puts all the slack on the top of the bar and makes it easier for the chain to jump off.
Changed the rim sprocket as per suggestion. Bought new Oregon bar and chain combo for a real low price on Amazon. Tree was about 20 inches across. When I put the second chain on I did check for oil being thrown off the bar before cutting with it.
Was cutting with the bottom of the bar. Got the dremel tool out and removed the offending burrs off the drive links- on both chains. Test pulled both of them on the bar and over the sprocket nose. Surprized how little metal it took to hang everything up.