10-year Blender user here (currently 2.79b, Win 10), facing a strange problem. I'm trying to export a selected object to STL, a routine action for me. I've boiled the problem down to a simple file containing one tetrahedron. When I select this tetrahedron and do Export --> STL with Export Selected checked, the resulting STL file is empty and will not open in another viewer (NetFabb).
Simple tetrahedron file here. (Google Drive, export-broken.blend, 622 kB)
Here are some cases that should help narrow down the behavior.
If I copy (shift-D) the tetrahedron, the copy also fails to export when selected. If I move the original tetrahedron to another layer, it properly exports to STL. If I make a copy, move the copy to another layer, and select both for export, the resulting STL contains only the copied+moved tetrahedron.
Exporting all (not just selected) works normally, even with just the original problematic tetrahedron.
Additional background: of course, I'm not trying to export tetrahedrons; I encountered this bug in the context of a much more complex file. I am preparing objects for 3D printing -- again, routine for me -- and exporting all is not an option. Anecdotally, it appears that this is not limited to STL export but also affects export to other formats. Moving an object to another layer in my more-complex file does not fix the export problem. The onset of the issue was not accompanied by any major change or issue I was aware of.
SOLVED (see answer below). The reason the object that is moved becomes exportable is that it was moved to a layer that happened to be set as visible in the second, minimized viewport.