I presume you are using a web mail because that is the only way that Firefox would have anything to do with email. If you are using an email program like Outlook, Outlook Express, Windows Live mail Program then the setting would be in there, not Firefox. There should be some place on the email page that gives you the option of staying signed in. In Firefox, you need to have 1st party cookies Kept. That would be located in Tools, Options, Privacy, Use Custom Settings for History, a checkmarks in Accept cookies from sites and NO check mark in 3rd party cookies.
You DO want 1st party cookies. You also would want Firefox to remember your browsing history, if you have it cleared each time you close it then you will always have to sign into every site you use that requires sign in.