I guess it depends on how far the edge has deteriorated before you touch it up. If the edge is just starting to pull then I might go to 8k, then a finisher (usually my J-Nat) and then strop. If its really bad then I might drop down to 3/4k and go from there.

Its better to start out with a higher grit and then drop down if you have to rather than starting out at 4k every time, as you'll save metal that way. You can always take more steel off if you need to but you cant put it back on!