Yes, except you have some sort of automated tool that does this for you. There are plugins for WordPress, Drupal, Joomla etc that automatically update your sitemap. If you don't use a CMS, there are other tools, like the Google Sitemap Generator (Beta) http://googlesitemapgenerator.googlecode.com/svn/trunk/doc/gsg-intro.html Code (markup):
If you use an appropriate plugin/tool that do this automatically for you then you don't have. I am using a plugin for me site that updates my sitemap everyday.
no, i think... based on my experience, i don't need to update my sitemap since it will automatically update itself whenever i access Google webmasters.