Should the Scrum Master be Permanent in his Position?

It is often a major concern of a scrum team that who shall be appointed to the position of the scrum master, and whether his post shall be permanent or rotated periodically. Mostly it is advised that the position of the master should not be rotated for several reasons. 

The first is that periodic change in leadership leads to an inconsistency in the output and productivity of the Development Team. Also, when the master is changed, the dynamics of the Development team and its specialization also changes. 

A permanent scrum master brings stability to the entire system. In certain scenarios, however, rotation of the job may be helpful, especially if the aim is to create learning opportunities to ensure that all team members are adept at doing the job. Sometimes, teams appoint different people for the job for different projects depending upon the expertise of their team members.