1) Check the setting on the plugin’s Settings page labeled ‘Are you using an Ajax powered theme?’. This should then allow the plugin to work with most Ajax themes.
2) See whether your theme or plugin has a “Reload code/script” settings field where you can enter code/scripts to be re-run when a new page is navigated to. An example of this would be the “Advanced AJAX Page Loader” plugin, which has a “Reload Code” section on it’s Settings page.
3) If neither of the above fix the problem then check your theme options to see whether you can disable Ajax loading either for the specific page that the Instagram Feed is on, or for your whole site. You may need to contact your theme author to ask them whether this option exists.