# is there upper limit on averaging window size for images?

An amateur question. I take an image and average pixels over a window 3 by 3, thus obtaining a smoother image. Then I increase the averaging window size - obtain an image with even less details, but still with some low frequency details. Is there some theoretical upper limit, when there is no sense to increase the averaging window anymore, because I will loose any details. If yes, does this limit depend on the range of intensities [0,255] or on lowest frequencies, present in the image?