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Hello. Thanks for the question.
I don't think this is something to ignore. If he's anemic enough to have shortness of breath, then it is clinical enough to find a reason and try to resolve it. Usually we can get an answer with routine bloodwork. If not, then we can do a bone marrow aspirate to see why there is anemia and whether or not the bone marrow is responsive. If it's not, then it may be an auto-immune condition or it may be leukemia or it could be infectious. No matter the cause, there should be something that can be done. In the short term, a blood transfusion would help his signs.
When it comes to supplements or diet to help, there is not a lot that helps. The one thing would be Erythropoeitin. This is an injection that can be given to stimulate the bone marrow to make more cells. I prefer to have my bone marrow aspirate done before giving it so that I know what's going on first. If the bone marrow is already responding well, then it's not needed. If it's not responding, then it could help.
If you haven't considered it, I would get a consult with a veterinary internal medicine specialist (Internist) to try to get some answers and a plan going forward.
I hope this helps, let me know if you have any other questions.