You add this influence permanently! It would be extremely difficult to reach 21 influence and to be elected consul for life, if you loose the previously gained influence... The only title that adds influence until you loose the title is the Pontifex Maximus, but it's an office that lasts until the senatore dies or is stripped of it, in which case, you loose the relative influence.
Gotcha! Yeah, in retrospect something seemed wrong. The only feasible way to get lots of influence is to be a successful Commander, and it was pretty easy to prevent people from commanding too much.
Thanks for the clarification!