I am not a big fan of term limits for anyone. If they are not doing a good job, vote them out. I prefer to fix the system by making the elections more fair by not allowing any party affiliation or incumbency on the ballot and opening up ballot access.
I am still considering banning any use of parties in committee assignments in Congress also. I have reservations about too many internal rules becoming part of the amendment but would add it if I have some reasonable way to word it. This combined with the ballot access would completely break the lock on government that the parties have, which means we can keep good people if we want.
Remember that the whole reason for term limits on the presidency was FDR. Washington did a personal limit of two terms (showing he was better at this than most and not power hungry). Everyone after him followed his precedence until FDR decided he could do a better job than anyone else and ran for four terms. Of course, he was elected since he was the first to discover how to bribe the voters in wholesale fashion with welfare and social security. He convinced people to blame the government for failing to protect them and then managed to convince them he could protect them. Afterwards, somebody who thought either this was wrong or there could never be anyone as good as FDR managed to get the term limit amendment passed.