I know if someone revives you with the Krauss Defibrillator it won't work that revive, but later it will. I've also heard after 4 downs you lose it. Correct me if I'm wrong though, I've only ever lost it after inactivity.
Well, I'm pretty sure it's the same for Die Rise and Buried, but I just did a test run on Die Rise and kept my perks. You get the laugh when you pick up the perk bottle which had me convinced I was wrong, but when I revive myself, I still have perma-tombstone.
According to COD wikia, being revived by the Krauss Defibrillator will cause you to lose all your perks in that instance, but not the persistent upgrade. Taking 3 consecutive downs without having any perks will cause you to lose the perma-perk.