I am glad to inform you all that we have fixed the API rate limit issue by verifying our business on Facebook and creating multiple applications to balance the API calls.
To fix this issue, here are the steps.
Update the plugin to latest version 4.4.0
Go to EFBL -> Settings -> Authentication, click on Get My Access Token button to get your very own access token and follow the on-screen instructions.
Go to EFBL -> Settings -> Clear Cache, Delete the cached pages.
No need to change any shortcode or widgets. It will keep working as it is, fancy, right?
Trust me, it was a long and complex process (yes, we kept working behind the scenes tirelessly days and nights when we first get this report) but we did it all as we have had the spirit and support from all of you lovely users of the plugin.