Thank you for the feedback. If any of these issues are not solved, please open a ticket at GitHub.

First: This sounds like the keepassxc-proxy that is transferring the messages between the extension and KeePassXC is shutdown. This might be due to anti-virus software or some other process that interferes with it. The next time this happens, check if the process is running.

Second: Please use as simple URL's as possible in your entries. If the site you're using is for example https://loginpage.example.com/login/something?yes=no, the best entry URL for this kind of page is https://loginpage.example.com/login/, https://loginpage.example.com (or just https://example.com).

Third: This means even after filling it doesn't regognize an entry from that page. Verify the page and entry URL again.

Fourth: Yes. It's very minimal. Notifications on why the filling doesn't work needs to be added so there's some indication to the user why nothing happens. If you've lost the connection totally, the icon should be gray with and X (or gray with a lock icon if database is closed).