Any dog with an auto immune disease - vaccinations are a big nono. You don't want to stimulate the immune system which is what vaccinations do. Also if a dog is on steroids, vaccinations do not "take" anyway. I can find info on this for you if you'd like.
From what you have said, the reduction of the pred dose had enabled the disease to take hold again, this is common - often vets advise reduction too fast. The steroid injection would only last up to 72 hrs, no longer - unless its something new that I'm not aware of.
He needs to be on a proper immunosuppressive dose Shona - which is 2 - 4 mg per kg per 24 hrs split into two doses, with a gastroprotectant to protect his tummy as steroids are very hard on the insides. If he is not on this dose, he will keep relapsing - I have seen it happen time and time again. If you reduce too early, he will relapse, again I've seen it time and time again..... each time they relapse its harder to get the immune system under control again, and you end up taking the pred dose higher and higher. Thing is there is a limit - and then you have to add in other immunosuppressive drugs like Azathioprine - which can have other implications long term.
I really hope the vets get it sorted soon,