Well, the last line of the message is self-explanatory:
Your MySQL server has gone away. 
Which means that egroupware ie PHP cannot connect to it.
This can have a multitude of reasons.
-Misconfiguration
-Loss of network
-Overstressed
This is not an egroupware issue, rather a server, software, hardware or
configuration issue.
I suggest you have a look in your server logs and find some hints there.
For further reading please consult the MySQL docs:
http://dev.mysql.com/doc/refman/5.0/en/gone-away.html
Cheers,
Ingo
