Sparton, regarding Aces High Eddie's Do Or Die skill, I've been keeping a closer eye on what it does, and I am even more convinced that the move prioritizes removing a beneficial effect over turning the endure status to permadeath. A few scenarios that I have confirmed:
-If endure is the only status effect, it removes endure but does not inflict permadeath (the remove beneficial effects part went first and after removal, there was no endure to convert to permadeath).
-If an enemy has endure and another positive effect, sometimes it will remove endure and not inflict permadeath (in this case, the remove beneficial effects part chose endure to remove). In other cases, it will remove both effects and inflict permadeath (in this case, the remove beneficial effects part chose the other positive effect to remove, and then it saw the endure status and inflicted permadeath).
-If an enemy has perfect immortality it always turns it into permadeath as intended, regardless of if there are other positive effects on the enemy or not. This is because perfect immortality can only be removed with permadeath, so it always fails the check for removing beneficial effects, but then is turned into permadeath afterwards.
I haven't encountered immortality or ghost regularly enough to test, but I have to imagine these findings hold true for that as well. The solution seems to be to switch the priority. Have the move check for endure/immortality/ghost first, and then after inflicting permadeath have it remove a beneficial effect.
Hope this information helps!