If your feed has previously been displaying just fine then randomly seems to stop working, it is most likely due to your access token expiring.
You can get a new access token by using the big blue button on the “Configure” tab.
We’ve received mixed reports of the frequency of the expiration of Instagram Access Tokens. Most tokens very rarely expire and never need to be renewed, but a few users have reported their token expiring every few days. All that Instagram’s documentation says is “Access tokens may expire at any time in the future.”.
If your token continually expires every few days then a potential solution is to create a brand new Instagram account for the sole purpose of obtaining an Access Token. For most accounts it seems that tokens don’t expire very frequently and so this may solve the problem for you. Simply create a new Instagram account and then log in via the plugin’s Settings page in WordPress, or using the button on this page, to obtain your new token.