Reproducible w/ trafficserver 5.3.1 and Stats over HTTP Plugin plugin.
1) Add to plugin.config:stats_over_http.so bf71886a308c1cf70cf05b6c5efbdd626a1156cc
2) Restart traffic server
3) Load this URL (yes, its the wrong URL): http://server_ip:port/_stats
Within 15 minutes the server will have consumed ~1.5K connections, trying to load this URL. Connections will continue to be consumed until proxy.config.net.connections_throttle limit is reached, at which point trafficeserver will not service any additional requests. At this point the only resolution is to do stop/start of trafficserver.