I hesitate to speak of stamina with regard to piano in the traditional sense, but there is a certain notion of physical stamina involved with piano playing, regardless of how efficient your technique is. In Neuhaus' book "The Art of Piano Playing" he states (i'm only paraphrasing here) that it's easy to play loud, it's easy to play fast, and it can be easy to play long. However, to play loud, fast, and for a long time is extremely difficult, and the greatest virtuosi achieved the stamina to do just that by developing it while they were young, with playing that was too loud and too fast, and so on and so forth. Keep in mind that a pianissimo is not the same in your living room as it is at Carnegie Hall, and so the minimum amount of volume needed to be heard differs greatly. As such, to play in a grand hall would be much more physically taxing than to play for a small audience in your home.
So yes, there is a certain sense of physical stamina in piano playing, however, if you have not built it up already, then I don't suggest actively attempting to train it.