Try the following: At the top right of the Thunderbird window, click the menu button ≡ > Settings - Calendar - Reminders Check the option "Show missed reminders for writable calendars".

I've have that checked all along. So that's not it. One new thing I noticed and I'm trying is I created a "show notifications for upcoming events" rule for "365 days after the event ends" under the Notification settings. I'm hoping that'll do it. Maybe Thunderbird's default is 1 month and if I make it a year, then the reminders will stay on the reminder list.

I'll know tomorrow if it works. I went back in time and created a test notification for April 16 and if it stays up past May 16 I should be good to go.

Thanks for trying~