“Is there anything within SQLYog that could cause SQL_LOG_BIN to be turned off for some statements?” NO.
SQLyog never executes SET sql_log_bin ON|OFF. You probably encountered a server bug. You did not tell the server version, but there are dozens/hundreds of reports at bugs.mysql.com about replication breakage with various versions.
According to http://dev.mysql.com/doc/refman/5.0/en/set-sql-log-bin.html also only a user with SUPER privilege can do it. Try connect with SQLyog as a user without that privilege. That will make it clear the it is not a client issue. It is server internals.
To debug this I think you will need to enable the server general log, reproduce it and isolate the series of SQL statements causing this. the same series of SQL statements would probably then cause replication breakage no mater from what client they are executed.