I wonder if you have a generic ANR headset, or one compatible with your particular aircraft - as all should be. In other words, most generic ones simply act in a broadband manner, whereas proper sets target specific damaging frequencies. The former run the risk of reducing sounds (audio cues) you want to hear.
Is it an analogue system, or a digital (programmable) one? With the latter, you plug it in before flight and dial in the aircraft type you are about to fly, and it blows the EPROM. Clever systems will give you the option of which seat; for example, front or rear crew in a helicopter.
Also, all ANR sets should be integrated with the intercom to ensure the performance of the latter does not deteriorate when the set is plugged in; or when some users don't have ANR and other do. The latter is perhaps the major design issue here as speech ineligibility changes enormously.
I suspect there are many who just get an ANR set at random and expect it to work in all environments.