This is a common issue and there is a bug in the game that causes this. This glitch could be caused by a large number of things outside of the game, so if you find the screen not responding it many not necessarily be caused by the game, but it is likely. There is a known bug where the game will stop responding to any touch input. The game will continue on as normal and track progress, but the game will no longer respond when you make any input.
This glitch appears to be caused by the battery saver mode. When you turn the screen upside down and then try to use the game again after this, the screen doesn’t seem to fully come out of battery saver mode. If this happens there is no other way to fix it other than close the game and kill the process. When you restart the game you should be able to play away as normal. For the moment it is best advised not to bother playing the game with battery saver mode enabled.