The Weekend Amulet is only offered after completing the lesson on Friday, as far as I can tell - you can't just buy them in the store, and they expire after the weekend is over whether you used it or not.
(I'm currently on an 872 day streak.)
The gamification techniques DuoLingo's used made it much easier to maintain the streak. Albeit, it was really easy to just do DuoLingo "to get it done" rather than focusing on it as part of study.
Now it becomes a part of my routine to practice German on Duolingo. Everyday for only about 10 minutes, and I like the Duolingo stories feature very much now and I can practice even for about 30 minutes on weekends.
That being said, I did learn quite some Spanish and I'm happy I did but I am not sure Duolingo (or Memrise for that matter which I also tried) works better than high school spaced repetition, Anki, or Pimsleur.
Looking at a global streak leaderboard doesn't help you improve your foreign language skills, so I'm not sure what "fell apart."
It's a flawed concept to build a leaderboard on a pliable statistic. That's what I'm saying.