So it turns out there isn’t anything wrong with my plug-in.
I’m not sure if you tried the Facebook Debugger tool, but I just used it and everything is good. Here’s a screenshot: https://imgur.com/JAYmBaZ
My plug-in help topics (Settings -> Facebook Thumb Fixer) has a section called “Occasionally it doesn’t work. What’s going on?” where this is explained with very simple instructions.
The reason this happens is because the first time your web page is shared on Facebook, they cache the open graph information as it was then. So the next time it is shared they retrieve the cached information. Using the Facebook Debugger tool forces the page open graph information to get re-indexed.
Something else worth mentioning is your homepage default thumbnail is way below the dimensions that Facebook recommends (1200×630 or 600×315): https://developers.facebook.com/docs/sharing/best-practices. This just means if your homepage is shared on Facebook it will only use small thumbnail instead of a full bleed image.
Have fun.