How can I set up Protected Pages so users only have to log in once?
Protected pages is really intended for one off password protection of webpages on a site. In order to have users login once to access a section of content, you should setup a user role assigned to a specific content type. 

In the case where your existing content requiring authentication is the same content type as the non authenticated content, you can use the TAC Lite (taxonomy access control lite) module. To restructure the existing site to use this:


Create a new taxonomy to distinguish the password protected nodes from the others
Assign your custom term to the nodes to distinguish that they need authentication to view.
Install TAC Lite module.
Setup a new user role to associate with viewing permissions for the nodes with the assigned term.
Configure TAC Lite for the node type with term and user role.
Remove protected pages passwords for the given pages. 
Clear caches
Test accessing (without login, you should see permission denied messaging) 
Optionally, install r4032login module to automatically direct nonauthenticated users trying to access this section to the login page, and subsequently redirect back to requested url. 


For future site builds or enhancements, I would recommend just setting up a distinct authenticated only content type and installing r4032login.