A serious difficulty with many kinds of non-reductive materialism in virtue of the fact that it denies a causal role to mental states. If physicalism is true, then only properly physical properties can play causal roles. David Lewis wrote the following, in an essay in defense of the identity theory:
[Epiphenomenalism] exploits a flaw in the standard regularity theory of cause. We know on other grounds that the theory must be corrected to discriminate between genuine causes and the spurious causes which are their epiphenomenal correlates. (The “power on” light does not cause the motor to go on, even if it is a lawfully perfect correlate of the electric current that really causes the motor to go.) Given a satisfactory correction, the nonphysical correlate will be evicted from its spurious causal role and thereby lose its status [...].