Check whether there is a UITabBar or UIToolbar below it. The problem is that most likely you try to show actionSheet as subview of your current view, which starts only above tabs and toolbar. However since actionSheet is always shown attached to bottom of the screen, you will miss taps outside your view.
The fix is to show your actionSheet in the whole application window, instead of subview of your current view:
UIActionSheet *actionSheet = [[UIActionSheet alloc] initWithTitle:nil
[actionSheet showInView:[UIApplication sharedApplication].keyWindow];