If you think there's a chance you may have suggested the site to a totally incorrect category (the cat was playing with the mouse, etc.), you may suggest the site once more (after moving giving the cat a toy mouse not connected to the computer) to the correct category, as suggestions to obviously incorrect categories are sometimes deleted, rather than moved.
However, odds are against it, even so. I believe the "official" advice (per the administrators of this site) is that you may resuggest the site, once, after at least 6 months. Sites do occasionally disappear without intentional editor action (the editor's cat was playing with the computer mouse, etc.), and sometimes sites just disappear without a trace. The odds of that happening twice, though, are astronomical.