I think the answer to your question is that it's not so much about playing by ear as committing the tunes to memory so that you don't need sheet music. I find that some tunes are more easily remembered than others, and I often have to study the sheet music to work out some of the more subtle bits that seem to baffle my memory. Once I have finally worked it all out, then I don't need the sheet music again. However, once in a while I'll come across a tune that I simply cannot memorise completely, and I usually just stop trying to play it. Or in other circumstances I can remember the tune, but as soon as I'm playing it on the accordion I suffer a memory lapse, and that does get very frustrating. Usually such tunes are also consigned to my memory's recycle bin.
It would appear that that some people simply cannot play by ear at all, and it isn't something that can be learned. For instance, I've often picked up the accordion, played a tune near perfectly on it by ear, then realised I had played it in the wrong key. I think this is quite common amongst "ear" players, who often play tunes in different keys. In my case it will usually happen because a difficult tune might be easier to play in another key, and I cannot be bothered to try and nail it in the proper key.
Try playing a tune you know well in a different key. I appreciate that's a lot harder for you PA guys, but if you can manage it, you should be able to try playing other tunes by ear.
