I had one of my sites suddenly go down with a SPDY_PROTOCOL_ERROR, all my other sites were operational so I knew 100% it was nothing to do with any certificate problem.
I eventually traced it to a permissions problem with the location for the nginx fastcgi cache. A simple
chown -R www-data:www-data on the
/var/cache/nginx folder resolved it for me immediately. Hopefully this may help someone in future.