I was always told to keep them closed when not in use. When asked why I usually got a few different answers. I think the one that makes the most sense is that in leaving them open the bellows very slowly work their way open. In most accordions made these days I doubt air leakage is serious problem but I wonder about the effect it would have on the bellows over time. I have played a few accordions that are never closed and when I finish playing them I try in vain to close the bellow straps and the bellows have stretched to the point that the straps can't catch.
Not really so stupid, and funny no one mentioned dust ... dust settles in the bellows' folds. Sometimes to a great amount over the years and it can be difficult to remove when hardened, maybe due to moist and soaking through water resolvable glue used, as seen often with old (piano-) accordions. I clean bellow folds occasionally with a flat slightly stiffish paint brush, as taught years ago by Concertina maker Harry Crabb Sr. - Nout
Some years ago, my first accordion was only decoration and it stood realy open for good looking a very long time (look at the foto at link 2). When I sometimes tryed to play it, it was very strong to shut and to play it. I needed a long time with muscels to get it in a playposition again. Now I shut my accordions always.
Klaus
I had a builder tell me to keep the bellows snapped when not playing due to the fact that Louisiana-built accordions can contain bacteria that can spread to your home if left unsnapped for long periods of time. He also said since Louisiana has higher atmospheric humidity, that it was important to retain the limited amount of humidity that was "built-in" the box. Everytime you play, you continue to lose small amounts of this humidity at a rate of 5 atm/1000 c-lbs of air, which after years of playing depletes the humidity. Once this occurs, your accordion will simply crumble apart.
When I finish playing, I always strap the bellows shut and store the accordion in its case. That way it is always protected from dust, pets, a clumsy foot ect.