Seeing a similar issue on a site I've set up. Server is running Ubuntu, PHP 5.5.9-1; have updated to latest WP (4.5.3). I'm running on a test installation, with multiple different sites; I've created a simple site with only 3 pages, which seems like it should be a quick and simple download, but no luck.
The page doesn't go blank like in the OP's description; it just gives the following under Activity Log:
[2016-07-20 21:59:41] thadboyd has started generating static files
[2016-07-20 21:59:41] Setting up
[2016-07-20 21:59:41] Fetched 30 of 30 pages/filesAnd then the progress spinner next to the "Pause" button spins forever. If I reload the page, I get the Resume/Cancel buttons and an Export Log with a list of the 30 files. The first two lines (the root page and wp-includes/js/wp-emoji-release.min.js) show "—" in the "Found on" column, and there are three pages with 400-series errors (xmlrpc.php, comments/feed, and wp-json/oembed/1.0/embed); other than that everything looks normal.
I've tried disabling all other plugins, changing max_execution_time from 30 to 120, and adding the two lines to the end of wp-config.php that poopshoot recommended. No change; the issue persists.
Let me know if you have any other ideas; thanks.