There could be a couple of reasons your Snapchat app is not refreshing, the most common of which is a problem with your network connection.
Check that you're still connected to the internet, and that other apps or websites are behaving as normal.
If this is the case, then the second most likely issue is a fault with your device. Try force quitting Snapchat, or even restarting your phone. It's an obvious solution, but you'd be surprised how many times it's done the trick for me.
Sometimes, an app is created with "bugs" or errors that don't affect the user interface, but might send your phone spinning off doing an infinite calculation or sending out a request and waiting for a response that will never return. The best thing to do is restart in this instance,
Finally, if nether of the above work - make sure you have the latest version of Snapchat. If you do, and you're still experiencing trouble, try deleting the app and reinstalling it.
If you're still having no luck getting Snapchat to refresh as it should - then get in touch with their support team via the website support.snapchat.com/