Try increasing the value of the max_allowed_packet system variable. Default size is 1MB but it sounds like you are exceeding this.
To set this add
To set this add
max_allowed_packet=64M(replacing the 64M with whatever value you require) to your config file and restart the server or log into mysql client and issue
SET GLOBAL max_allowed_packet=67108864
Note: Value in the config file can be followed by M, K to specifiy mb or kb but when using a SET command the value must be given as bytes or as an expression (eg you could specify a 64mb max_allowed_packet using SET GLOBAL max_allowed_packet=64*1024*1024).
Hopefully this should resolve your problem.
Sorry forgot to mention that mysqldump also has a max_allowed_packet option and you should try setting this in addition to the above when you run mysqldump. Just start mysqldump with a --max_allowed_packet= option.
Source: forums.mysql.com