FindChessboardCorners cannot detect chessboard on very large images by long focal length lens

A few points.

1. Down-sizing, as you noticed, helps the detector. That is because the corner-detection filters used in OpenCV to find the corners have fixed size, and that size of convolution mask may be too small to detect your corners - the full-size image may actually look "smooth" at that scale, particularly where it is slightly blurry. However, by downscaling you throw away some corner location accuracy.
2. For the same reason, sharpening helps too. However, it also goes against accuracy, because it adds bias to the subpixel positions of the corners - even in the ideal case with no noise. To convince yourself that this is the case, consider the 1D analogue: the intensity of the image around a corner (in 1D, a sharp black-white transition) looks ideally like a sigmoid curve (a ramp with smooth corners), and you want to find the location of its inflection point. Sharpening makes the curve steeper, which in general will move that point's location. Things get worse when you take into account that sharpening generally amplifies noise.
3. The likely correct way to proceed is to start at a lower resolution (i.e. downsizing), then scale up the positions of the corners thus found, and use them as the initial estimates for a run of cvFindCornersSubpix at full resolution.