Hi David and welcome to the forums!
That’s interesting–sorry for the trouble here because that’s definitely not how we would expect the events calendar to behave.
Do you happen to use caching on your host or site? If so, are you able to disable it and/or clear the cache for your site? I saw the message that your site uses cookies and that gave me a hunch that the site is capturing and displaying old information as well.
And, of course, it would be great if you could follow our standard troubleshooting steps as well to see check for theme and plugin conflicts as well.
Let’s start there and see what we find. 🙂
Cheers!
Geoff