This is important: Daxman, has a tick panel already been run?
If not, insist on it -- demand it, if you have to. Today!!! You need to rule out Babesia.
We are seeing a ton of Babesia (tick disease) in my area: it attacks RBCs and mimics auto-immune disease. The symptoms are indistinguishable, but Babesia is curable with meds.
It's emerging as a "new" problem in my area (though it's an old one in other places), and vets in my don't know to think "tick disease" for those symptoms, so they just assume it's an auto-immune problem. Any time we are getting low RBC or low platelets on bloodwork, the rescue I work for is now sending out a tick panel to see if there's Babesia -- we have 3 Babesia-confirmed dogs in the rescue, in a state where "officially" we're not supposed to have any of it at all.
Ask your vet while waiting on the panel results to come back to please look at the RBCs on a slide and look for the parasite -- there are CDC images on the web to use as a guide. It's VERY hard to see as it's a tiny thing inside the RBC, but someone with a good eye can often find it. The head vet tech at my clinic is a rock star at finding it -- then the lab results are used to confirm.
This is so frequently mis-diagnosed that a friend's dog nearly died -- under the care of a board-certified internal-medicine specialist. He said there was no hope. I begged her to go see my vet for a second opinion before giving up. My vet saved her dog by properly diagnosing the Babesia in the nick of time.
PM me if you need help. The fact that pred isn't working makes me suspicious that you're dealing with something else entirely -- with the rescue, I've been down that road and lost dogs to what we thought was untreatable autoimmune until we realized what was really going on. Now the dogs are turning around in 24 hours with near-normal bloodwork once the right meds are on board--which have to be special-ordered (it's malaria meds!).