We just finished installing and testing an enhanced image handler program on the server to resolve some occasional glitches people were having when uploading and attaching images. Looks like that nailed the problem.
Premium tech members (Professional Appliantologists, Senior Appliantology Fellows, and Master Samurai Tech Alumnus) can attach images of unlimited size to posts. Even with this setting, members would sometimes get an error when attempting to upload even a modest sized image. We squashed that bug!
Many thanks to @coolhandluke for bringing this to our attention!