How important is it for SEO to have an up to date sitemap for an online marketplace?

It is essential to provide Google with a constantly updated sitemap, especially for large sites. If the sitemap generation takes a long time you can divide it into several pages, containing a limited number of links, and update only the section that includes newest and updated contents.

I agree with what was previously said. It will be time-sensitive but worth it if you implement a system to update your sitemap automatically in the future. Also, a solution might exist for your platform that will save you time.

Dividing your sitemap using a sitemap index will also 1. help diagnose possible indexing problems via Webmaster Tools 2. force you to review your site architecture which can lead to valuable insights to improve your site.

Relevant article on the subject: http://www.distilled.net/blog/seo/indexation-problems-diagnosis-using-google-webmaster-tools/

....and....

At the end of the day your sitemap is "just a file" with the links to all the files on your site. It is one of many items on your good SEO/website checklist to do and shouldn't be ignored however.

The SEO guys may scream in pain here but there are lots of sites that rank fine without a sitemap because they are doing damm fine in other more important areas.

There are lots of automated ways to make sure that your sitemap is up to date and doesn't deliver bad results and once you automate it you should in theory be able to "virtually walk away".

Put simply and as you can likely guess from the name a sitemap is a map of your site’s contents. Google has a helpful page here that briefly explains what a sitemap is, what formats they can take, and what they are used for a good read if you are encountering this term for the first time. Sitemaps typically take the form of a long list of links. Some sites have HTML maps accessible to all visitors (look in the footer for a “sitemap” link), while others rely solely on an XML file that is submitted directly to search engines. The current accepted standard is to at least have a sitemap in XML. Having a visible sitemap page is optional.
The navigation you have added to your store’s header and footer are for shoppers trying to find their way around. Whether you have menus, links, search boxes, or all three, these functions exist for humans. Sitemaps, on the other hand, are not meant for humans at all. Although your shoppers certainly could use them to find a specific page or destination, their primary purpose is to help search engines index your site. A sitemap tells a search engine “these are all the pages available here.” The search engine is then able to quickly add these pages to its “index” basically, the giant library of every website and individual page it knows about — and review its data to determine which search queries it is relevant to. If a product page is included in your sitemap, a search engine can easily find and index it, which means shoppers looking for something specific from that search engine will be able to find it, too.
In my view it is especially important to update sitemap for an online marketplace. If a sitemap is not useful to your shoppers, you might not see much of a point in having one. Also, it’s true that search engines can crawl and index your store without an XML file, so if your site is small, you might not see the use. However, even if you have an exceedingly small store, there are several advantages to providing search engines a sitemap instead of assuming they will crawl and index your site over time. Why wait for them to come to you when you can force them to show up? Without an XML sitemap or even without a manually updated sitemap page — you might run into the following problems:
1. New pages can take a long time to be discovered, especially if they aren’t linked heavily from other product pages.
2. Your product images might not be included in image search results, because they’re largely dependent on sitemaps to be indexed.
3. Updates you make to pages might not help your rankings for a long time, because you aren’t providing search engines with valuable metadata (including when the page has been updated).
4. The fewer links your map-less store has, the more likely it is to be excluded from searches, because Google doesn’t yet know about all of your pages, your store’s relevancy, and whether or not it can fully trust you. Essentially, all these SEO little factors add up.
The long and short of it is this: without a sitemap, search engines can and will still crawl and index your store for inclusion in search results. But a sitemap makes the process much, much faster.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath