Hi zimm,
You’ve got some good guesses so far, but let me throw this out there as food for thought. Your tool holder looks very similar to the Tormach parting tool holder from LMS that I have, except mine holds the blade horizontal, with no rake, and has a “T” on the end of the model number, 250-007T. I’ve used it on 2 different bench lathes over a couple of years and haven’t had any problem with it or the blade. I use a 1/16” P type, HSS blade that is .041”+/- thick at the bottom edge. I line it up vertically in the tool holder and cinch it down. I’ve used it on aluminum, brass and steel rods, up to 3/4” diameter. I would have to guess that (1) you aren’t getting the blade aligned vertically in the holder and (2) it may be digging in due to the rake built into the tool holder and/or (3) the blade is just too thin at .012”. Did you double check that measurement?
Maybe reaching for straws a little with this question, but do you lock down the carriage when you part off?
Tom