To find out if the feed is working ok...
To test whether your feed is updating normally:
1) Create a new post (any post will do) and note the title.
2) Access your RSS feed and do a search on this title (you can use CTRL+F or CMD+F on a Mac to initiate a search in the page). The new title should appear inside the <title> tag, on top of your feed with the appropriate publication date (visible under <pubdate>).
Here are a few things to check if your feed is not updating.
Check if your feed is cached
Enabling cache is the recommended method to improve your overall website performance and SEO. Enabling cache will result in the server storing your page as static content or even on site visitors' browsers, and present visitors with the stored copy of the page (without querying your database). The downside of this method is that this page may not be up to date (yet) with the most recent content. Since RSS feeds are time sensitive, it should not use any Cache.
If you're using a plugin such as the W3 Total Cache plugin or any other tool to cache your website pages, make sure to disable cache on your RSS feed page.
If you're publishing a large volume of content, your feed could end up being pretty large and heavy to load. This can cause external services to timeout / fail when accessing your most recent content.
To avoid this, simply restrict the maximum number of posts stored in your feed. If you use WordPress for example, you can control this from your Admin settings as shown below. No need to have hundreds of elements in there; 10-20 most recent items should be enough for most users.