Since you're using a submission program -- which, by the by, I would urge you not to do -- you are probably not talking about subscribing to the likes of Inktomi and AltaVista. That being the case, you should only resubmit if there are major changes to the site.
For the most part, spiders will hit your site regularly (even if not often), so constantly resubmitting when there are no changes would not only put you into danger of being considered spam, but would be pointless.
In the SEO world today, there really aren't too many SE's that need submitting to. The directories need a hand submit ($$ except ODP), the major search engines crawl pretty good(fast, google, lycos) the ppc sites need a hand submit ($$), the pay for inclusion people need a hand submit ($$) and AV with their ransom note need a hand submit.
So basically you need to hand submit when your funds and/or time run out for you pay sites. As far as monthly hand submitting to the search engines, I'd say this isn't necessary if your new site is linked from a site that is in their database.