Not unless your titer goes up. When you are initially diagnosed and treated, you will have a high titer level, such as 1:128, following successful treatment, this will begin to drop. Over a 6-12 month period, a four-fold drop is generally expected (so 1:128 goes down to 1:32), and it continues to decline, slowly, for they years to come. If your titer level suddenly went up, such as going from 1:10 -> 1:64, that indicated reinfection. It is also possible for the initial treatment to fail, with a similar indicator.
TLDR: As long as the numbers continue a downward trend, no further treatment is generally required. If they start to rebound, however, then you get to look forward to another round of overly large shots of penicillin g procaine. If you get tested at the same facility each time, they will have your previous results and will make sure everything is OK. If you go to a new place, you may need to let them know that you previously had it, and low-level titers are expected.
I hope this answers your question satisfactorily.