There have indeed been a few reports of folks ending up with an empty zip file. I’m releasing a new version of Simply Static (v2.0.0) in the next couple weeks that I’m hoping will fix this issue, or at least make it easier to determine the cause of the problem.
I’m interested in this as well – commenting to follow the discussion. I just found Simply Static and would love to use it, but this is blocking that. Happy to donate if the new version of the plugin works with my version of WP (4.7).
FYI, v2.0 of Simply Static has been released. If you could give it a try and let me know if it works I’d greatly appreciate it. I’ve heard from one person so far that has having issues with zip generation and v2.0 of Simply Static fixed it.