You can resharpen the convex part by using a strop on a forgiving piece of backing.
One approach:
Take a piece of quality, straight, flat 2x4. Cut down to say 18" in length. Find an old computer mouse pad with a rubbery backing. Cut to shape of 2x4 and glue down.
Now find some 240 and 400 grit sandpaper (play with different grits). Cut sandpaper strips so they fit on strop, leave them long, just put one end under the board, loop over and across top of board.
The soft backing will conform to convex edge if you do it right. Push edge down into soft backing, goal is to obviously maintain the convexivity on existing edge, and pull the knife towards you (don't push the sharp edge into sandpaper, pull towards you).
Hope that helps. Takes a little practice, not much, this coming from a guy who can't use flat stones but likes the jig and V-crock sharpeners.
(thanks to Cliff Stamp for genesis of this idea).
[This message has been edited by rdangerer (edited 03-12-2001).]