The question was about saving passwords, not session ids.
Passwords are sometimes stored by a separate application in an encrypted store.
That might be what SkipStone is expecting to have available.
But the general thought of stored passwords in a device like the Kindle does not seem like a very secure place. (Although there is a variation of Sqlite that maintains an aes encrypted database file. I seem to remember it being added to BR about a year ago.)
Save the password in your mind, learn to remember it.