Sharing of login cookies with Automator

I have an Automator services workflow that downloads the New York Times crossword each day.

After upgrading to El Capitan, it no longer works. When I opened the script to figure out what broke, I found that Safari no longer shares the login cookie (since the NYT's site requires an account to access the puzzle) with Automator.

The error I get is under Download URL'S. "Could not download (URL). You do not have permission to access the requested resource"

I logged into the URL in Safari and made sure "Remember me" was checked so the cookie would be set.

Is there any way to restore this functionality?