Is there any particular condition that would ban you from flying?

Infections: Any communicable disease transmitted by breath/cough/ sneeze can be denied access to plane travel. If a person appears too ill to sit upright in the seat and follow crew instructions, they can be denied travel. Usually a public health advisory for serious disease or epidemic changes the airlines policies/enforcement. Medical assistance during travel ( example, oxygen) needs precertification.

Yes: Some airlines have restrictions for women flying later in pregnancy - may be as early as 28 weeks for some airlines and medical certificate may be required. If you have active TB that would not be allowed. As epidemics occur - restrictions are likely to change.