open a ticket with support ..that would be my next step.

EMC suggested to replace the director, but since there is no alarm nor any malfunction on director, I feel there is a simple communication issue and I want to know how to troubleshoot the root cause.

Sometimes when you have an NC director the ethernet chip on the director is blown. From a host point of view it will work fine and service all I/O. There is also a serial port on the director as a backup should the support center try to recover the director. However you should have it replaced.