Depending on the site, one can usually find a "Keep me signed in for two weeks" box somewhere on the log in page. By clicking on that box, you allow your browser to SAVE your log in info, keeping you from having to sign in so often.
One thing though, it's not recommended one do this if one shares the computer with other users as they too, will have access to your mail if you don't sign out of your account.
I have been experiencing the same problem as you. Did you ever resolve it? What is the solution? The answer that someone gave you did not help me because like you, I click that box saying "keep me signed in for two weeks" and it DOESN'T WORK!. Meantime I still have to enter my name and password several times a day like you said. I actually called Verizon support and the tech support person spent close to an hour with me and it was no help. AHHHH! I need help from someone who can provide the correct info. It shouldn't be that difficult.