It is my impression that Verizon does not intend to offer the two-week login option again. I do not know that for a fact, but everything I have seen seems to indicate that Verizon views the two-week login as a serious security threat. And no, I don't know why, I used the two-week login for years, worked fine for me, and I hope I am wrong and they do bring it back.
However, there are a couple of easy ways to deal with this:
1) Rather than starting your browser each time you want to access Verizon webmail, just open webmail once in a separate tab or separate browser instance and then simply don't close that tab or browser instance until you are ready to shut down your system. This way webmail will remain open, although after some period of time (it appears to me to be 20 or so minutes) a pop-up will occur asking you to click if you want to continue with webmail:
I have left that pop-up showing for hours and still been able to access webmail with that one click.
2) Use an automated login tool. I use the older free version of KeePass to access and log into many websites, and have set up a KeePass script that will automatically access the webmail URL and then enter my user name and password (took a little work to get the number of tabs and the delays needed for it to work). The only thing I have to do is open a new tab before I start the KeePass script (I am using Firefox, but it should work for Chrome or IE, probably Safari). This way I can close and restart the browser, or reboot the system, and once the browser is back up log in again without manually entering anything other than three clicks - one to get a new tab and two to run the KeePass script. I am sure that many other password tools offer some form of automated login that you can use.
Now last, I would strongly suggest that everybody consider using an email client rather than depending on the webmail interface. There are lots of free email clients for all of the various operating systems you might be using, and these clients automate accessing the email servers and logging in. Plus they offer far greater editing capabilities, and since they download the emails to the system's hard drive you won't lose your emails if Verizon screws something up. I use the free Windows Live Mail client, I chose it 5 years ago when I first got Windows 7, and I have installed and used it on Windows XP, Windows Vista, Windows 7, Windows 8, and a preview of Windows 10 (supposedly generally available later this year).
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Justin
FiOS TV: Extreme HD, Internet: 50/50, Digital Voice
VMS Enhanced Service: 1 server, 2 clients
Keller, TX 76248 (VHO 1)