If you are using the setting show/remove posts that contain these words or phrases, otherwise known as the includewords/excludewords settings, you may be filtering out too many posts for the feed to display any. Instagram does not send posts from a specific user that also have a specific hashtag so the plugin will request all posts from the user account or hashtag feed and then will filter based on includword/excludeword. Here are some possible work arounds for this:
1) Raise the “Max concurrent API requests” setting
This setting will retrieve more posts initially to help with the filtering issue. Find it at the bottom of the “Customize” tab for Instagram Feed.
2) Use a “hashtag” feed and the “showusers” setting
If the hashtag you are using to filter the feed is fairly unique (not a lot of Instagram users post to the hashtag) you may have more success filtering a hashtag feed by user. Example:
[instagram-feed type=hashtag hashtag="#myFilterHashtag" showusers="myUserAccount"]
3) Use a “single” feed to show individual “single” posts
If you only have a few specific posts you’d like to display and it doesn’t change often, you can use the “single” feed type to display a feed of specific posts. See this post.