I have this same issue on an S5. The logs fill up with ~85MB over several days, filling the device entirely. At that point, the S5 shows as being on the network, but is basically inoperable.
There are three ways I've found to get the printer back into an operable state:
1) Factory Reset
2) Cura Connect Reset
3) SSH into the printer, and clean the log files directory, then reboot the printer (via the CLI)
Once one of those three steps is taken, the printer will be operable again for between 2 and 10 days, at which point the cycle repeats.
The root cause appears to be network connectivity issues - the printer appears to have network connectivity issues when under load (the laptop next to the printer does not exhibit any connectivity issues, and the printer is showing full signal). I see excessive avahi logs, as well as the printer's software having trouble getting firmware version information, or hitting its own API, causing it to log large python stack traces.
Long term, it would be great to get a more stable network connection, as this has other issues (Cura will frequently not be able to show the status of the print, despite the printer thinking it has a network connection - this will come and go as a print is operating). Short term, monitoring the size of the log directory and removing old files, or modifying the rotation settings would be a great help.