The "Top Day" sorting option does this, but posts fall off a cliff rather than falling off gradually. My understanding is that they'll remain on the page from hour 0 to hour 23, but then completely disappear starting in hour 24.

Instead of that, it would be ideal to implement a mathematical formula that pushes pages higher into the rankings with every upvote, comment, or view it gets, but pushes posts lower in the rankings with every additional hour passed. You have to tweak the specific parameters of that formula to get it right, but it essentially forces posts off the page after enough time has passed, while introducing new posts to replace the old. Unlike the "Top Day" sort where things are a step function, the idea with this is to make it gradual so that a popular post falls from #1 overall down to #2, then #3, etc. over the course of a day.