SSMS - using remember password option and save passwords
SSMS - useful tool for a SQL Server DBA and user to manage their work in SQL Server. This tool has been fine tuned since the RTM release of SQL 2005 since Nov.2005 and you may be aware using this tool you can manage SQL 2005 and 2000 instances without any issues.
IF you are on a Windows domain network then for the day-today work you must use (universally accepted) Windows Authentication logins that will help to avoid explicit provison of a password to SQL Server. If you are running in a Windows Domain, IMHO that's the easiest workaround for your problem. This is also the safest route with respect to security - any saved password is a potential security threat. Note that even in workgroup environments you can use Windows Authentication with local Windows logins if Management Studio is running on the same machine as the server.
Say in the case of using Mixed mode authentication on the servers that are impossible to deploy with windows authentication, you have to save the information and connection entries if the PC is commonly used in a development enviornment. TO accomplish this work-around to the problem, you can save off a copy of your local c:\Documents and Settings\{you}\Application Data\Microsoft\Microsoft SQL Server\90\Tools\Shell\mru.dat file. When management studio overwrites your saved password with an empty string like you describe, you could close management studio and then copy your backup mru.dat file over the more recent one. This will reset the saved settings of the connection dialog and other "most recently used" items in the UI to their saved values.
Please note the SSMS does encrypt the saved password but has no capability to make it secure, there is a method of decrypt such password mechanism in this current cyberworld.Be sure to restrict access to your saved mru.dat file to help prevent unauthorized access to your server.