I do not understand how your SOTO is dying. I recommend trying a different tactic(s).
1. Try leaving your pet stashed somewhere. I know that is not at all in the spirit of the class, but it is effective.
2. Talk to your healers. Dont blame them, talk to them. As I play a d/wd healer too, I understand that druids get shafted as their group heal, MEF, does not heal the warden pets, whereas the priest group heal does. I have also observed my Chiron standing right next to the priest, but not get the effects of group heal. Also, I found out that some healing addons do not refresh the pet's info very well. So I ask the healers to cast an occasional regen on the pet, whether it looks like it needs it or not. Also, in the standard game you have 6 individual focus slots, as well as 6 raid focus slots. Those do refesh the health status, so the healer setting the pet as one of those might help.
3. Use pet actions.
4. Wardens have a skill that heals their pet,
Elven Prayer. I agree the skill is not so spectacular, but it is there.