That code represents years of tweaks, fixes and obscure workarounds. There are countless problems that you will re-introduce with a code rewrite, because the subtleties in aged, thoroughly-used code are not immediately obvious.
Oh, but Jeff Attwood said . . . Whatever. And then Jeff Atwood said something very different.
Blah, blah, blah.
If the engineer that wrote the code isn't at the company anymore, and no one really gets it now, rewrite it. At least you will have some chance of understanding the new bugs instead of failing to understand the old bugs (and there are bugs in that old code that you, for whatever reason can't read.)
Rewrite. Always.