Thanks again for your feedback,
Indeed I had a restart script that runs at 5am every day, since I've had the problems with the zimbra.
I ran the fixperms script, thanks for the tip, and disabled the restart script. I'll try it without it for a while.
Concerning the disk space:
I believe it's normal some values are 0% free
zimbramail:/# df -a
Filesystem 1K-blocks Used Available Use% Mounted on
tmpfs 1681872 0 1681872 0% /lib/init/rw
proc 0 0 0 - /proc
sysfs 0 0 0 - /sys
tmpfs 1681872 0 1681872 0% /dev/shm
devpts 0 0 0 - /dev/pts
simfs 151187140 107137888 36369384 75% /
Edit: tonight, same thing
Can I post some log file?
zimbra@zimbramail:/$ zmcontrol status
zmmailboxdctl is not running.