I believe the degen continues increasing past -10, though the fastest your minions will ever degenerate life is 20 per second, or 10 pips. This only really comes into play when you use a skill like Verata's Aura or Healing Breeze on your Minions. As it is, I've had minions that didn't really get healed with Verata's Sacrifice, but I've never managed to get them to survive much longer than that- healing them just becomes too much of a hassle.
It's generally possible in PvE to have your minions survive a couple of battles, so long as they don't get focused too heavily in those battles. I'll keep my minions around for 1-2 battles, and when they start becoming difficult to keep alive, I just throw death nova on them, as you said. Keep them alive until they get up to the next group of enemies, and let them die