The way the Gmail extension works is it saves the URL to the email you're adding. If you're currently logged in to multiple Gmail accounts, Google will add a number to the URLs to identify which account an email is associated to. The number simply reflects the order in which you logged in to those accounts. (See the example below)
If you logged in to your personal, work, and freelance Gmail accounts, it would be associated with these links:
- personal - https://mail.google.com/mail/u/0/
- work - https://mail.google.com/mail/u/1/
- freelance - https://mail.google.com/mail/u/2/
Notice the number at the end of each URL.
If for some reason, you re-login in all of those accounts but this time in a different order, the numbers will then be associated with a different account.
- work - https://mail.google.com/mail/u/0/
- freelance - https://mail.google.com/mail/u/1/
- personal - https://mail.google.com/mail/u/2/
Before the change of login order, the link
https://mail.google.com/mail/u/0/#starred/158bf0e7285ae8ad would have pointed to an email under the personal account.
After the change of login order, it will now point to the work account. Since the link opens up a different Gmail account, the email will not be accessible anymore.
To make the links work again, you just need to log back in the same order when you added those emails as tasks.