Is this Auditory Processing Delay?
Research into auditory processing deficits is a minefield and there is no real consensus as to what is and is not a deficit in auditory processing. Further, and possibly more relevant for individuals with, or dealing with, a processing disorder, is how to treat/manage the disorder. Again, unfortunately, there is no real consensus on the issue. Ferguson (2009) presents a relatively non-technical overview of the issues.

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Ferguson MA (2009) Diagnosing Auditory Processing Disorders. ENT News, January/February.