With the simplest Miller compensation (capacitance Cc located between stage N and stage N+1), if the right-half plane zero created by the Cc is too close to the unity-gain-bandwidth, then the system phase margin is effectively reduced. Because the purpose of Miller compensation is to ensure a sufficient phase margin to reduce ripples or oscillations, phase margin reduction is a sign of Miller compensation not working.

When the gain of opamp is small

It should work all the time