I leave the same litter on for three or four melts. It starts getting funky looking by that time, and is breaking down into finer granuals. It's cheap, so change every melt if you want to.
'Litter contains organic elements, so is a flux itself. As I have said before, I use a dry piece of dowel to stir completely to the bottom, and to scrape the sides of the pot. This way, the carbon thoughroly saturates the mix, rather than just the top layer. You just plain ain't gonna be able to stir something with a lighter specific gravity down into the lead otherwise.