there is a spring loaded pin inside the mirror mechanism which is supposed to stop the mirror from turning once it reaches the correct position. it might be the pin is jammed or the spring inside broken which causes the mirror not to stop at the correct position.
unfortunately there is no way one can reach this pin without dismantling the mirror completely. BMW has made the mirror such that it cannot be fixed back after dismantling as there is a flanged tube which is holding the 2 movable parts in place. once this flange is destroyed to break the mirror into 2, there's no way to fix it back unless you can find a machine shop which can create this kind of joints. the other way is to have some ingenuity and use a long nut and bolt with some spaces to join the 2 parts back together.
most of the time, paying for a replacement mirror is easier.