If I've reached the point where stropping isn't quite doing the job, I'll go back to a grit selection comparable to the level of the original (working) finish. For some who prefer a coarse edge, that might imply a coarser grit (maybe 220 through 400). If the edge was more 'satin' in finish, that might be in the 400 through 800 range. If the edge was polished, I'd start up around 1000+. Point being, there's no benefit in starting too low in grit, to get the edge back to 'stropping shape' again. Starting too low will remove more metal than necessary, and will also require much more work to get back to the original finish. Start as high as you think might accomplish the task. If that's not quite enough, only then take a step down in grit. Just enough to get the job done, no more.