I don't know if its Thunderbird or if its Windows doing this but it's irritating.

Quite possible neither. I would suspect other third party software like ccleaner or an anti virus or some sort of optimizer.

Nah, I don't use anything like CCleaner or any other optimizers, and the only anti-virus I run is Windows Defender. I've never known an anti-virus software to remove shortcuts and leave the app intact, especially without even a notification.

I've noticed often when it disappears, after I've re-pinned it and run it, it will update before starting.

Still nothing, huh?

It's just done it again. Lasted almost three whole weeks this time, at least.

Have you tried resetting the taskbar icons?

https://www.tenforums.com/tutorials/3151-reset-clear-taskbar-pinned-apps-windows-10-a.html