It could be done!!
I could create a small bounce mod for you.
Let me know which kind of pets you want to stay longer.
Like item based:ancestral warriors from items like Key of Elysium or doppelgangers Dvalin's Simulacrum.
or skill based?
Also how many pets you want to spawn at a time?
Limitations of the concept:
1) Cant keep them up forever. But they can be kept alive for like 10mins 30mins or 1hr.
2) Recharge time will have to be longer as well, other wise the undying pets will crowd the area.