MySQL Master - Slave replication stops after 20min with no errors
The first thing I would do is check the network between the Master and Slave. Why ???
Almost 8 years ago, I wrote this post : Slave I/O thread dies very often
I once had an occasion where I saw a Slave with SHOW SLAVE STATUS\G looking exactly as you have it, but it was not replicating. This is what actually happened:

The firewall on the Slave would become intermittent
The Master could not talk back to the Slave through the I/O thread
SHOW PROCESSLIST on the Master revealed that the I/O thread was no longer there
Slave assumed the Master was OK

What I recommend is this

Start troubleshooting the traceroute on dynamic....org
See if DNS is acting up. If DNS is involved, add skip-name-resolve and skip-host-cache to my.cnf on Master and Slave and restart mysqld

Please let us know what you found in your troubleshooting