Nah, I've done this before cause I'm one that wants my balls to look nice. Usually I've found the "flush" logos like Brunswicks, MoRich and Visionary for example will last a long time if not forever. The ones that have "indented" logos like Storm, Columbia/Track, AMF, Ebonite/Hammer etc can come off. The old Hammers (Faball) were the worst. Storm finnaly upgraded thier paint and way of engraving but they are one of the worst ones also.
What I'd advise is going to an arts and crafts store and buy paint pens. They work the best. You can also buy the little paint bottles but beware on the kind cause you don't want paint that can't tolerate too much moisture or paint you can't use on multiple surfaces. Then get some small brushes.
Your also going to need sandpaper. Get 600 grit, 800 then 1000 at Wal Mart in the auto and paint section, or some auto part stores sell them. Your also going to need some polish depending on the final surface you want. Paint it over the logs and it's ok to let the paint get around the logos. After it dries, if you have a spinner, use the sandpaper. If you don't, put it in a sink with a little water running and sand it in circles on 4 sides of the ball. Repeat with the 800 grit then 1000 then use the polish with a cloth or sponge, wipe it hard and in circles with paper towels. May need to repeat a few times to get it to a gloss. Then wash it off with water and glass cleaner with a towel.
Walla, brand new ball!
