Technically you don't need to resubmit the sitemap. Technically you don't even need to use a sitemap. Search engines use many ways to discover your content. They prefer to discover new content by following links, they also use RSS feeds and toolbar data. If your content will not be discovered through those ways then you should think about using a sitemap.
I don't know all the details of your personal situation but I would speculate that it could be a good idea if you updated your sitemap every 1-2 weeks.
You could try a simple experiment. Don't update the sitemap and see if the content is indexed. That will let you know if you really need the sitemap or not.
thanks for your reply goodroi..! Btw you are right... my content got indexed without updated sitemap. This shows that even if the sitemap doesn't get updated your content may be indexed by google. Anyway fortunately my sitemap plugin is also working fine now :) So there is no problem at all!
BTW Goodroi can you tell me what are the file permissions for the file sitemap.xml and sitemap.xml.gz ?