You can't open and close the file; it is not thread-safe (thread one closes fp and sets it to NULL and sleeps, thread two wakes up and uses a NULL fp).
And you can't wrap the open/close in a CRITICAL_SECTION, because logging happens at shutdown, CRITICAL_SECTION relies on a destructor to work properly, and you can't control the order in which C++ destructors are called during shutdown.
I learned all that the hard way a few releases back.
You can rotate the logs using the "copytruncate" feature of logrotate.