No, you do not need to resubmit your sitemap. Once you've submitted it once, Google (at least) will periodically reload it to check for updates. For example, in "sitemap details" for my site in Google Webmaster Tools, I see the following status:
"This Sitemap was submitted Dec 3, 2010, and processed Apr 21, 2012."
I can assure you that Google did not take 17 months just to process my sitemap once. :)
In fact, you don't need to explicitly submit your sitemap even once — all you need to do is include a Sitemap: directive in your robots.txt file. The next time any search engine that supports the sitemap protocol visits your site, they'll parse your robots.txt file, notice the sitemap URL and fetch it.
If you want to, you can also actively notify search engines when you update your sitemap. The sitemap protocol specifies a standard way to do that by sending an HTTP request to a "ping" URL. This may be useful if you want to minimize the delay before the updates are noticed.