I too have started facing this issue after updating my iPhone 6S to 9.2.1. The animations stop working suddenly. When I restart the phone then the problem is solved but after 1-2 hrs again the problem starts. I am also facing the following issues in my phone-
1. The animations and transition effects stop working suddenly
2. The list of songs in Music app goes blank. I just see white screen when I open the app. It reappears when I force quit and restart the Music app.
3. Opening the Health app causes the phone to switch off and it shows the low battery sign even though battery is 49-50%. I have stopped opening the Health app now because of this.
4. Sometimes while messaging the message box above the keyboard acts weird. it will hide or show only partial message. Once I hit send the whole message will get sent.
5. Camera freezes when I open it sometimes. have to force quit it and restart the Camera app for it to start working again.
6. I'm on a 3G network. And suddenly my 3G signal will stop and I just get 2g then. It shows E for edge in the top row.
All these issues start to happen simultaneously. When I restart the phone all will get resolved. And then after 1-2 hrs they will start again.
Its Pathetic to see Apple release an update that causes a 2-3 month old iphone 6s to act like this. There was once a time when each update was thoroughly beta tested before release. But now every update is a leap of faith.