I am frequently required to sign-in in order to access my e-mail. I check the box that is supposed to keep me signed in for 2 weeks, but it never works. The next time I attempt to access e-mails, I have to sign in.
When you check that box to keep you signed in, it updates your Verizon.com cookie that's stored on your computer to keep you signed in. If that cookie gets deleted, then it wont remember next time you go there. Your browser settings may be set up to delete your cookies when you close your browser or you may have another program on your computer deleting cookies regularly for you. So make sure that your settings or other program does not delete your Verizon cookie.