In parliamentary systems, term limits almost always apply to the Head of State, both directly and indirectly elected. The same idea of avoiding a perpetuation in power therefore applies also to the Head of State in parliamentary systems. It is true that his/her powers are mostly ceremonial or representative in nature but in a republican State a perpetuation as a Head of State, particularly if directly elected by the people, could mean a greater role and a devaluation of the leadership that the prime minister assumes in such parliamentary systems.
The longer the time in office, the stronger could be the temptation for the President to abandon his/her role as super partes arbiter and enter into party politics.