Hi Scott,

It depends if you want those new pages to be indexed fast. If you want them to be indexed as soon as possible, is a good idea to make a new sitemap because the next time bots crawl your web, they will find new pages easily and then can index them. If indexing new pages is not urgent for you, then wait.

Obviously, if you create a high number of pages which may be indexed per day, create a new sitemap each time you have a new page could be a hard work.

You have to stablish your needs, for example a new sitemap/day, or a new sitemap/10 new pages, etc.

If you use some CMS, like WordPress, there are some useful plugins that allow you automate this task.

I hope my answer would be helpful.

Only a plus to Adam's response: remember to design custom 404 pages. It's a good idea to include links to pages you want to rank, a search box or a list of featured pages (post, categories, etc.) At least, it may help to keep users staying in your website.

Hope it helps.

Sergio.