Which Roman office was designed to be held for six months and never renewed?

The dictatorship - a genuine constitutional office, not a term of abuse. In an emergency the Senate could have one man appointed with unrestricted authority for a maximum of six months, or until the crisis passed, precisely so that the usual system of paired magistrates checking each other did not paralyse the state under threat.

It mostly worked, and the model case is Cincinnatus, called from his plough in 458 BC, given absolute power, winning the campaign in about sixteen days and resigning to go back to the farm. The office had built-in limits: a fixed term, no authority over the treasury, and the appointment made by others rather than seized.

Sulla broke it in 82 BC by taking the post with no time limit and using it to conduct proscriptions - published lists of citizens who could be killed for a reward. Caesar then took it for ten years and finally for life, which is what got him stabbed. The word survives with Sulla's and Caesar's meaning rather than Cincinnatus's, and the American habit of invoking Cincinnatus as the model of relinquished power runs directly back to the earlier version.