out of a few typical testimonies I can think of, most are unproven(so useless to try and conclude anything), and a good deal come from using the wrong method to look for something. like trying to hear a difference between 2 sounds by using sighted evaluation with long delays between the samples. or looking for taste preferences with an abx test ^_^.
I see 4 big groups but I'm sure we could make more sub groups:
1/ recognizing something in the music where the brain uses memorized patterns to identify them. human speech, a guitar, a "realistic" cymbal. all coming from the model we already have stored from previous experiences. that's not really hearing, but of course it can have a drastic impact on the things we will notice. once we have identified/memorized a given pattern, it will be much easier to recognize it again. like how listening to a song many times makes it easier to recognize the song when we hear it.
2/ conscious search, like trying to find out if there are 2 or 3 guitars playing. 1/ can help for sure, but the most obvious is that we need to ask ourselves that question before we can hope to answer it. if you take 10 people and ask them to count the guitars, they will obviously do better than if you let them listen and only afterward ask them how many guitars were playing. that's asking ourselves a question and concentrating on that one thing. IMO if the guy notices something on his own, it's not transparent, if he doesn't then it is transparent(for him). if I need 3years of training to recognize a wine from another one, maybe I shouldn't bother about the difference in the first place.
3/ identifying a change in air pressure. also known as sound. the only situation where we're looking at actual hearing ability IMO. if something changes too slowly or too fast, my ears may fail to notice it(5hz or 25000hz). same with amplitude, if the variation is too small I may also fail to hear it. that's actual hearing and it won't get better after I have spent 3 days listening to the same song again and again.
4/ placebo. given enough time, every memory will fail enough so that the same sound now feels like it was different a long time ago.
if we look for something particular in a song(like 2/), then of course more time can help, just like how given enough time you will find waldo in the picture.
but if we look for any sort of audible variation between 2 sources, then the best method seems to point toward short samples and rapid switching instead of longer time. I honestly don't know if having a long time for such a test can help for anything. my educated guess is no, but only because with more time we soon fall into the "memory loses accuracy over time" problem. so depending on what you're looking for, I would say that more time could end up being a handicap as it will increasingly move us toward 4.