Without optimization, Nginx defaults to allowing a maximum of one worker process with 512 connections and 60s timeout. 20 unique visitors per second will lead to 500 errors in less than a minute.
It does not matter how fast the backend is. A persistent HTTP connection will last 60 seconds following the latest client request, unless the browser goes out of its way to explicitly close the connection.
P.S. OP's website uses Apache but the same issue of overly conservative limits still apply.
Are you sure? My understanding was that nginx would fill up all free connections up to the max, but then would begin draining idle connections so it could create new ones for new visitors.
