Why won't nginx accept more than 1024 connections from apache bench
@Terra almost had the answer that wound up working out.
accept_mutex off;worker_connections 4096;
I tried adding each change, by itself, and reloading, but I still saw the same error. It wasn't until I changed both, that I could push past 1024 connections.
It seems like, because of the proxy, I need to have twice as many worker connections, as I intend to accept.