Sometimes the Pulse RSS feed reader that was included with the Fire gets stuck and will not update.
Currently the only option to get this to fix itself is to force the app to close. The way that we do this is that we swipe the gear at the top right corner, then click the more link, then click on the applications link.
From there we can see a list of all of the running applications , third party applications, or all applications. The best thing to do is just to leave it at running applications, and scroll down to Pulse - or whatever app you want to force closed. At the top of the page, right underneath the name of the app there will be a button that says "Force Stop" click this button and the program should shut down.
Now go back to the home screen, and choose the app again, and it should refresh like normal.
Don't forget, you are not limited to the suggested sites that Pulse provides to you. You can search for your favorite sites RSS feed and add it to your Pulse feed. *Not all Pulse features will work with out an internet connection (such as images or videos), so if you use your Pulse feed for reading material on the subway, as I do, sites like The Art of Trolling, which is mostly a photo blog will not display the images while you are not connected to the internet. Also, not all sites syndicate their entire content on their RSS feed, many will only provide just a portion of the articles or posts that are on their website. While you have internet connectivity this is not a problem, you can just click through to view the entire post/article, however reading in an area where you do not have an internet connection will not allow you the ability to view the entire post/article for all RSS feeds (just something to keep in mind)