Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Max has had shortness of breath for the past two weeks that does not seem to be improving on its own.
A normal cat has a resting respiratory rate of about 10 to 15 breaths per minute, and one breath is considered the in and out motion of his chest. If he has a rate consistently faster than 50 breaths per minute then he is in trouble.
If you can notice that he is breathing abnormally then I am concerned for him, as cats normally hide things very well until they are so sick they can no longer do so.
Cats that cannot breathe or exchange oxygen normally often don't eat well, or burn excessive calories trying to exchange oxygen so his weight loss and change in appetite is not surprising.
If he doesn't have a nasal discharge and isn't sneezing then his difficulty breathing is likely related to a problem in his chest or secondary to anemia (decreased numbers of red blood cells).
Problems in his chest leading to an increased respiratory effort include primary heart disease (including cardiomyopathy and heartworm), lung disease including asthma, bacterial, viral, parasitic (lungworm) or fungal infections, a mass(es) in the chest including lymphoma, heart based tumors or carcinomas, or fluid around the lungs (pleural effusion) due to a mass, bleeding, chylothorax or an infection.
Anemia can be secondary to poor red blood cell production, either due to kidney disease as the kidneys make a hormone to stimulate production or primary bone marrow disease, or anemia can be due to bleeding or destruction of red cells due to a tumor, blood parasite or autoimmune disease (body attacks its own red blood cells and destroys them).
If your fellow's tongue and gum color are a nice bubblegum pink them he is in better shape then if his gum and tongue color is blue or gray, these would signify he is real trouble and this is a true emergency.
The conditions I listed above are serious and I would highly recommend that your fellow see a veterinarian promptly to have an examination and further testing done based upon his examination. Max likely needs radiographs of his chest to evaluate his heart and lungs to start and then further diagnostics based upon those findings. That may include testing for heartworm and lungworms, aspirating fluid for examination if there is fluid present around her lungs, or blood titers for fungal infections as well as blood tests for hyperthyroidism and organ failure
In the meantime keep him quiet so he can breathe as easily as possible.
Please let me know if you have any further questions.