mysql_insert() first opens all affected tables (which implicitly
starts a transaction in InnoDB), then stat tables.
A failure to open a stat table caused open_tables() to abort
the current stmt transaction (trans_rollback_stmt()). So, from the
server point of view the following ha_write_row()-s happened outside
of a transactions, and the server didn't bother to commit them.

The server has a mechanism to prevent a transaction being
unexpectedly committed or rolled back in the middle of a statement -
if an operation takes place _in a sub-statement_ it cannot change
the transaction state. Operations on stat tables are exactly that -
they are not allowed to change a transaction state. Put them in
a sub-statement to make sure they don't.