My situation may be different. I have a brain lesion, and different "hearing" problems.
I have always been very musical, and at one point was fairly proficient on several instruments at the college level. I sing a cappella in church. However, for all practical purposes I cannot play by ear, and I can't sight sing alone. I can't really memorize music either. I'm pretty sure that my problems are a result of information processing issues. I was diagnosed with information processing issues in regular neuropsychological testing, and figured out the rest. I hear music just fine, but I don't understand what I hear. In other words I experience the sensation accurately. I can play in tune very well in a good group, and can play with subtlety. However, beyond very simple things, I cannot identify the notes or harmonies I hear. I have trouble listening to a melody and singing it back. I can remember all the "ups" and "downs", but get the "distances" wrong. Most people, even if they don't "know" what they are hearing, can repeat melodies and even memorize them very well.
I think there are two reasons for this. First, most people are better at processing information than I am. When I hear the melody, I hear it accurately, but it doesn't "sink in" enough to allow me to recall it accurately. Second, because I'm not processing it enough, including encoding it in my memory, it's very hard to identify a certain interval I hear as a "major 3rd", or "major 6th". (You may not be familiar with the terms, but it's very basic stuff. Most people do it instinctively.)
I figured this out when I was working with an ear training program. I was practicing "intervals", which are two successive notes, or pitches, played one after the other. I found that if I tried to identify intervals only by listening my accuracy was very low. However, If I forced myself to focus on the first note very hard, and then actually sing both notes out loud my accuracy improved tremendously. It took some concentration. By singing the notes I gave my brain the chance to "understand" or "interpret" the sounds I heard. Some things went from impossibly obscure to plainly obvious. I had been hearing everything just fine, but I wasn't internalizing the pitches to the point where I could imagine or sing them easily. There was a disconnect between my hearing (the sensation) and my understanding.
I don't know if this is your problem, but I could see how someone might have a similar problem with language. They might hear the other person talking just fine, but the automatic interpretation of the physical sounds into meaningful words might not take place the way it should. If you were having a simple partial (aura) that part of the brain that interprets language might not be functioning right.
