MySQL master-slave replication over an unstable internet link
Increase some of these:  net_retry_count, slave_transaction_retries, slave_net_timeout.
Monitor the slaves to catch them in the case of a really long network break.  Then do SLAVE STOP; SLAVE START;
Make sure expire_logs_days is long enough so that you won't lose binlogs.  There is no "too big", except that you could eventually run out of disk space.


Everything should work find after the Slave gets going again.  (There will be a delay as it "catches up".)