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First guess, server maximum memory issue...

Pretty high maybe, but memory is not only used by CGSI.

The fact that resizing the image makes it work tells you it's probably is memory issue.
Further: realize that source image is left untouched at the server. So large images will take disk space.

CGSmartImage works fine on large images. I just tested CGSI resizing the same 4200x2800 image numerous times on the same page, and had no difficulty. Must be a problem on your end.