As a follow up to the previous post, I have now confirmed that in the latest release it all remains the same for me. The pet will die regardless of super damage being on or off outside of gamma burst mode, whilst in gamma burst it simply cannot die. The new respawn feature if fine, but as the pet is knocked down in TVHM Mayhem 3 immediately outside of gamma mode, it doesn't really help.
Maybe you can provide a savegame with easily repeatable instructions.