Do you play on an older phone, by any chance? Because this is very likely a memory issue. The game keeps up to 25 previous messages in the log and for some reason this seems to take up a lot of memory on mobile devices. As far as I can tell, this is an issue of RenPy (the program I'm using to code the game) rather than CH itself. I might reduce the maximum amount of messages further, though. That way it should have less on an impact on older phones.
Thanks for letting me know!