Churg-Strauss syndrome can cause Vasculitic neuropathy

Churg-Strauss Syndrome if you also have eosionphillic esophagitis

Churg Strauss Syndrome is a rare systemic autoimmune disease characterized by inflammation of small to medium sized arteries, arterioles and venules. This inflammatory process of blood vessels is more commonly known as vasculitis. Churg Strauss vasculitis is characterized by the invasion and abnormal increase of a white blood cell known as an eosinophil. The eosinophils cluster together and release harmful granules that collect in different parts of the body as inflammatory nodule lesions. This is called granulomatosis. This eosinophilic inflammation, along with asthma, are the hallmarks of Churg Strauss Syndrome. The inflammatory process can cause impaired blood flow to various organ systems. The resultant damage to different organs may be temporary or permanent.

Churg Strauss Syndrome should be considered when there is late onset asthma, or worsening asthma, along with either numbness or pain in the extremities, sinus problems, a lingering cough, a rash, stomach problems, or symptoms of cardiac involvement.

Asthma, hay fever, sinus pain and inflammation, weight loss, loss of appetite, fatigue, cough abdominal pain, gastrointestinal bleeding, rash or skin sores

Mepolizumab (a monoclonal antibody against interleukin-5) is a safe and well-tolerated therapy that will allow for steroid tapering in patients with steroid-dependent Churg-Strauss Syndrome (CSS).

There is nothing which says it causes hair loss, but can be that in some cases you experience it.