MySQL 5.6 Slaves Fail to Reconnect to older MySQL server when it goes down for backups
While replicating from a MySQL 5.0 Master to MySQL 5.6 Slave is allowed, it is not good to keep that scenario indefinitely. Why ? The way MySQL 5.6 reconnects to an older Master may be more difficult with older Masters.
To illustrate problems of this nature, consider how MySQL Replication can break between versions because of Binary Logs changing between versions of MySQL. I have discussed this before in my answer to the Jan 02, 2015 question mysql replication master 5.5 slave 5.1 error on create database.
In that answer, I mentioned how binary log events have been added with each new major release of MySQL. This may call for MySQL 5.6 to ignore or bypass events from the binary logs it does not understand. In some rare cases, the SQL will break while trying to unravel and binary log event that may have changed between versions. In that instance, the SQL thread for MySQL Replication WILL NEVER START BACK UP.
While I am talking about the SQL thread in my scenario, your situation involves the I/O thread. There may some issues (bug or untested feature) causing reconnects not work. In light of this, a Slave reconnecting to a Master of a previous version of MySQL is no longer a trivial matter.
There is a current bug report for MySQL 5.6.20 that has been triaged since August 2014 (Bug #73494 : Slave can't reconnect after 2003 error when sha256_password is used). This is not directly related to connecting to a older Master but the problem exists with MySQL 5.6 itself.
You should either consider one of the following

Increase max_allowed_packet to 1G on the Master and all Slaves
refrain from using MySQL 5.6 as a Slave to an older Master
upgrade to MySQL 5.6 across the board

UPDATE 2015-05-21 18:06 EDT
If Master and Slave have max_allowed_packet set at 16M, then there is no need to change it.
If you can live without changing skip-networking, try the following

Step 01 : STOP SLAVE IO_THREAD;
Step 02 : Run mysqldump --single-transaction ...
Step 03 : START SLAVE IO_THREAD;

This way, the I/O Thread stays connected 24 / 7 and you never have to restart mysql.
GIVE IT A TRY !!!