That Instagram widget has been touchy right from the beginning 2 or so years ago. When I used the Original plugin long ago and Davinci theme I cut it right out of the theme file and replaced it with a shortcode for a 3rd party Instagram widget.
"Thanks for the patience. I inspected the site with Chrome's dev console and checked the Error log in the cPanel, but was not able to find anything specific logged for the instagram widget, which suggests that the error is occuring on application level and not on server level.
I had a look online and found similar reported issues with the same message that you get, this is why I advise you to check with the developer and provider of the widget and ask them to review the problem that you have as they best know their product"