The first I thought about was what max_allowed_packet actually controls. Here is what I found:
According to the page 99 of "Understanding MySQL Internals" (ISBN 0-596-00957-7), here are paragraphs 1-3 explaining it:
MySQL network communication code was
written under the assumption that
queries are always reasonably short,
and therefore can be sent to and
processed by the server in one chunk,
which is called a packet in MySQL
terminology. The server allocates the
memory for a temporary buffer to store
the packet, and it requests enough to
fit it entirely. This architecture
requires a precaution to avoid having
the server run out of memory---a cap
on the size of the packet, which this
option accomplishes.
The code of interest in relation to
this option is found in
sql/net_serv.cc. Take a look at my_net_read(), then follow the call to my_real_read() and pay
particular attention to
net_realloc().
This variable also limits the length
of a result of many string functons.
See sql/field.cc and
sql/intem_strfunc.cc for details.
Given that definition of max_allowed_packet, I then discovered something else from ServerFault: innodb_log_file_size and innodb_log_buffer_size combined must be larger than ten times your biggest blob object if you have a lot of large ones
Keeping these two things in mind, I would increase innodb_log_file_size in /etc/my.cnf to the max size allowed for it, 2047M. This of course requires the following
service mysql stop
rm -f /var/lib/mysql/ib_logfile*
service mysql start
This will accommodate any big blobs you may have in your data.