I always click "Remember Password" when connecting to a database server.
Sometimes when I come back into SSMS, it has it remembered, sometimes not. More often it does not. I regularly connect to about 4 different servers, it's fairly random when it works for which servers.
How can I get this to work all the time?
Yup this is a known bug in SSMS - I believe all versions, reported here on connect. I have experienced it in the past, yet had machines that never had any problems.
I would love to say I have a solution for it, but unfortunately the solution for me was to allow windows authentication for connecting instead.
My recommendation is to post on the bug report and if enough people do it Microsoft will either fix it or provide information about it. Yes, they do pay attention to connect bug reports when they get 'popular'.
I found this link on the connect link provided by eddiegroves.
It is a tutorial that shows you how to create a new server registration. I've added one, restarted SSMS a couple times and it seems my password is still there...