Instagram has applied some new restrictions in order to show a feed a on website. It's now necessary that you create your own feed app and make it compatible with your site. In order to create an instagram app, please read the instructions here https://github.com/adrianengine/jquery-spectragram/wiki/How-to-get-Instagram-API-access-token-and-fix-your-broken-feed
Start from step 1 mentioned into the link above. Ignore step 5 and 9.
Note: it's important that when creating the APP, you must be logged in with the same account that you wish to use to retrieve the feed.
The app you create will only be able to show the feed from the account with which it has been created. For example, if your instagram account is JohnDoe, the app will only be able to show the feed from JohnDoe.
Once you've generated your Access Token and client ID, copy and paste them in Theme Options -> General Settings -> Instagram access token & Instagram client ID