I have reinstalled KeePass and firefox addon, and now it does not connect to KeePass. Re-installation and wiping helpless - still no request for authorization.
On my other PC everything works as expected.
So, the question is how to restore connection between Firefox and KeePass?
I would first check the KeePassRPC and Kee settings for a match between the port and the security level.
And then I would temporarily include in the settings of Kee logging into the browser console with level Debug and see if there is something related to Kee and its connection to KeePass. This should give you a start point to fix your problem.
Sorry for my English.