Ask PG: Can you please fix the connection resets and / or explain them?
It's usually accompanied by HN slowing down and returning a page in 6-10 seconds or so.
My guess is (but I really am poking in the dark here) that it has something to do with the accept queue overflowing and the network stack sending out RST packets (I've seen those using tcpdump so they figure in there somewhere).
Alternatively the 'listen' gets dropped.