MySQL RDS Slave stop replicating
Judging from the comments and your update to the question, it looks like the case where the data being loaded from legacy system is taking too long to be applied to the SLAVE.

Without the information on what your binlog_format is set to, I can only assume that it is set to ROW. You can try setting this to MIXED and then the SLAVE updates should run a lot quicker and not lag behind the master unless there are other factors affecting the SLAVE being slow.

When logged in as a privileged user, run the following from MySQL client:

SET GLOBAL binlog_format='MIXED';

If the above resolves your problem, then add this to your /etc/my.cnf to make it permanent across MySQL restarts.