Building on Rand au'thor'srand al'thor's great evidence, I think that, while it's possible that some Victors visit the Capitol for prostitution throughout the year, it doesn't present a plot inconsistency if the only time the Victors return to the Capitol is as Mentors during the annual games.
The 74th Hunger Games lasted 18 days and the 25th Quarter Quell lasted the longest at 27 days, plus at least a week of prep and training.
It's perfectly credible that Victors could develop close friendships in the month or so they out of every year that spend in the Capitol during the games, especially considering that they share a uniquely traumatic experience that no one else understands, and that they likely don't socialize with Capitol citizens unless they have to. That gives Chaff and Haymitch something like three weeks of drinking nights a year with limited access to other friends and a terrible, stressful job that few other people understand. It's no wonder they're drinking buddies. It's also part of the Mentor's job to build alliances with other Mentors and their tributes, further encouraging close relationships.
It's possible that the majority of Victor prostitution takes place during those couple weeks when they're already in the Capitol and back in the public eye. It's also a Mentor's job to secure Gifts from Capitol Sponsors, which might be part of the agreement. From what we know about the Capitol's trend-based economy, the most demand for Victors would be when they're back in the spotlight during the annual games. It's possible that some rich citizens might keep especially attractive Victors like Finnick in town year-round, but that's likely the exception to the rule.