Sorry to see that you're having trouble.
There are usually two things that are the problem when this happens.
1) There is either a plugin or your hosting company that is using caching. You can try clearing the cache or contacting your host about ignoring the Instagram Feed in the caching system they use. WP Engine typically has an aggressive caching system if that is your host.
2) You are on of the rare, unlucky people that has a WordPress installation that doesn't clear temporarily cached data in the database. We have a setting that has a workaround for this though. Go to the Settings page, "Customize" tab and scroll down to the bottom and change the option "Force cache to clear on interval" to "Yes".
Let me know if either of those work for you. Also, if you are still having trouble. Could you send me a link to the page you are having trouble with along with the "system info" from the "Support" tab?