Oops, I had the numbers for the hits backwards.Even if the convict uses theirs right away that gives us three days. With 8 people and the possibility of losing two people per night (lynch + convict hit) it is very unlikely we ever make it to the point where there are no more hits. That doesn't account for the betta hits either.
Convict role gives us at least two days of hits so long as they stay alive. Heck, after tonight we could theoretically be without hits if both the convict and betta are gone anyways.