Heroku restarts their servers once every 24 hours with only thirty seconds' warning. Since the games are in-memory, this of course kicks everyone out of whatever games they may be in the middle of.
I guess the solution is to have the games be on Redis instead of in-memory? I'm a bit more front-end oriented so I was bewildered to learn this was how it worked in the first place and I'm not 100% confident in my solution.