It's permanent. You can sharpen the same weapon once per skill lvl. And you can try this (never did it myself) - SAVE!
1. Unlearn the skill with cash
2. Learn it again and try to re-sharpen the same weapon => does it work?
Actually, I didn't even look at the weapon type, just right clicked and looked for the "sharpen option", was fun for me. Is more fun than sharpening my pencils <img src="/ubbthreads/images/graemlins/silly.gif" alt="" />
Kiya
A nice sharpen thread, click here, explains this cheat