The only reasons I'm aware of not to go directly from developer to fixer are fixer longevity (acid fixers will gradually lose their acidity) and the potential of fogging if the pH gets high enough for development to continue with the developer absorbed into the emulsion (thiosulfate is a weak foggant). Given your stop bath is acidic enough to stop development promptly, I don't know any reason you couldn't reuse it. Then again, there's nothing gained, as far as I can see, by doing this...