LCD suddenly stops displaying
Not really a common problem. But the problem is that the display is used in write-only mode, so you can't read the status of it. What's worse is that 4-bit mode is in use, so any glitch on E wire will make the display to receive wildy different command and data bytes than expected, as the high/low nibbles are mixed. What might solve this is that periodically, like every second or every time the screen needs to be redrawn, it is properly reinitialized again.

It is also possible that the MCU write timing is on the edge of what the display can work with, so sometimes it might might just not see a write properly.