I received the Fanatic badge a while back. Today I've been on the site for another 100 consecutive days, but I haven't earned the badge. Looking over the list of all the people who've gotten this badge, no one has it 2x. Is it impossible to earn this badge twice?
No, you don't get the Fanatic badge twice. You didn't get Enthusiast 6 times for 180 days either. There's no badge beyond Fanatic; all you get is the increasing “consecutive days” number in your profile.
The badge FAQ on the main meta site explains precisely what it takes to get the various badges, and mentions which ones can be obtained multiple times.