Convex edges are a breeze to maintain. Simple stropping technique (edge-trailing), but done with coarser grit (how coarse/fine depends on how much refinement the edge needs to begin with). Wet/dry sandpaper from 3M or Norton (aluminum oxide and/or silicon carbide), on a backing of leather or similar soft(ish) material attached to a hard, flat backing (such as wood), are all the materials you need. For light touch-ups, start with something like 1000/2000 grit. If the edge is a little too dull for that to be effective, you might start at 400/600. If you want to completely re-do the bevel, a more aggressive grit like 220 would be a good starting point. The great thing about the sandpaper is, it's available in many grit stages (at least 220/320/400/600/800/1000/1200/1500/2000, and more if you really want a very high polish). Choose what works best for you.
Keep the sharpening angle as low as possible, and the pressure light. This will help to ensure against rounding the edge.