Skype for Mac doesn't remember my password

Since my password is stored in a password manager, this also involved opening up the password manager vault to get to just the Skype password and sign in.

How do I get Skype for Mac to remember my password?

By clicking Sign me in when Skype starts

If you are on the latest version of Skype, it supports sign-in using Skype Name or Microsoft account.

If you select, Sign me in when Skype starts it automatically stores the password and logs you in the next time. This worked fine for me on the latest version just now.

On version 7.17 (377), you get the option to select this option from Preferences

sdayals answer does not seem to apply anymore for the latest version of skype as of today. Here is the solution:

When logged into skype, go to Skype -> Preferences -> General and tick "Sign me in when skype starts"