Hello erinstellato .
On June 19th you wrote:
@Pablo_Lerner Thank you for sharing your list. With regard to the password issue, that's a difficult one to track down. Passwords for SSMS are stored in Windows Credential Manager. There is a limit to the number of credentials that can be stored, so there is a possibility that the limit is being reached. The next time a password doesn't appear when it's been saved, check Credential Manager to confirm the connection exists there.
This does not explain the issue because the issue is not "some connections do remember the password but others do not". The issue is the same connection, to the same server, using the same user name and password, sometimes SSMS remembers the password and sometimes it does not. Which means either sometimes SSMS is looking for the password in a different place or it sometimes fails to reach Credential Manager. Any way, since sometimes the password IS found and remembered by SSMS it means that it IS present in Credential Manger.