Could it possibly be just the actual size of the button that it making it difficult to 'press' accurately?
You say that it works without your menu. Your menu takes up a not insubstantial width of the screen and without the menu, the gallery and, in particular, the Thumbnail Button would be larger.
You also say that if you zoom and hit the Thumbnail Button just right, it also works.
These both suggest that if the button were larger, then it would work for you most (if not all) of the time.
The fact that increasing the 'z-index' did not work suggests that there is nothing on top of the gallery (eg. an invisible part of your menu) that would prevent the Thumbnail Button from working.
In fact, I have just viewed your 'Flowers' gallery on my iPod Touch and, on my first attempt, have managed to hit the Thumbnail Button 10 times out of 10 (after selecting 10 separate images individually) with no fails and without zooming.
SimpleViewer Support Team.