Is it possible that takayasu's can "burn out". if not what is alternative treatment...?

Probably not.: If I understand your question, takayasu's disease is arteritis and will not "burn out". This usually a large vessel problem and can result in fibrosis. Follow with your PCP for monitoring your prognosis,

All autoimmune diseases can "burn out" but given the potentially disastrous complications if the disease is not treated, Immunosuppressive medications are routinely given for Takayasu's Arteritis. After signs and symptoms have improved and imaging modalities show control of disease, medications are tapered and can be discontinued. Whether that is considered a "burn out" is semantics.