Ah that was useful. Apparently nginx is rate-limiting my own IP address:
2018/05/17 04:48:41 [error] 312#312: *5257301 limiting requests, excess: 100.873 by zone "bot", client: xxxxx, server: _, request: "POST /admin/email/handle_mail?api_key=xxxxx&api_username=system HTTP/1.1", host: "blenderartists.org"
This is uncharted area for me; any thoughts on how I can fix this?