Could it be possible that dark matter is emitting EM radiations on a scale that is not known or perceivable by humans yet and undetectable by man-made instruments?
A type of radiation that our instruments were just not designed to pick up on? Being insensitive and not advanced enough? Thus we do not yet have all the pieces to solve the puzzle?
Edit: We need to remember that there are infrared and gamma rays on either end of the spectrum and we are aware that dark matter is definitely not emitting visible light, or any of the other type of EM waves. Considering that gamma rays were discovered roughly only a hundred years ago, isn't it possible that the spectrum could be further extended on either side and that we're still not aware of it?