If it really makes water into hydrogen peroxide, then it would sanitize very effectively for a short time. Peroxide breaks down really quickly as it sanitizes. So if that's really the case with this sanitizer, then I definitely would always make a fresh batch and not try to use old sanitizer solution.
Oh don't give me none more of that Old Janx Spirit
No, don't you give me none more of that Old Janx Spirit
For my head will fly, my tongue will lie, my eyes will fry and I may die
Won't you pour me one more of that sinful Old Janx Spirit