I did see some reports of similar behavior in some old 4.5.x cases. In a couple cases it occurred following an OS update.
In each case the problem resolved itself after a midnight rollover (as you described for one instance) or it was resolved following a restart at the next maintenance.
As a precaution, check your eventor script to make sure it has not been modified.
You should find the following lines within:
touch $outfile
chmod 644 $outfile
At the next EP restart ensure that the out directory and log files are at the expected permissions prior to restart.
Correct as needed.