Well you can have your settings as such that one payment for an ad will last xx amount of days...even 365 days or more..and as a property is rented out, the ad can be paused, but not deleted.. so effectively you could republish the original ad without the need to re-create it, or of course your customer can pay to relist the ad using the user dashboard.
The out-of-the-box ClassiPress product does not have an option for a membership style fee system though, and at present you can only charge per ad. I believe there are others who have looked at membership type plugins but I can't say for certain if anyone has it effectively up and running. Potentially it is something you could customize though if you have the coding knowledge to work it out.