Please don't consider euthanasia until you have exhausted all possibilities!
Please refill the Carafate Prescription and use the entire time that he must be on prednisone and doxycycline. I would also ask the vet for an anti-emetic (anti-nausea) medication such as Reglan or Cerenia, and I would add Pepcid (at a human dose) to the protocol. Please give the Pepcid at least one hour away from the Carafate.
Auto-immune anemias take months to correct but most of them do result in normal blood values. Patience is important. Other possibilites include 1. other infectious diseases that are not sensitive to Doxycycline, so a broad infectious disease profile should be performed, 2. GI ulceration and Heliobacter Pylori infection, 3. GI cancers, 4. Other anemias caused by parasites and toxins. 5. Misc. causes.
An abdominal Ultrasound and X-Ray, and barium study may also be helpful. Please also feed Liver, Heart and other organ meats, at least temporarily.
Ginger is an anti-emetic herb and would help with vomiting also.
Vomiting blood is an emergency. I do hope he's been to the vet since you wrote this note. Did the vet mention any possibilities the last time you took him in? Can you get more medication for his stomach? If the med helped before, perhaps that's the answer then - a problem in the stomach. But they'll have to do more testing to determine the exact cause and I hope, cure it.