I'd then check your splunkd.log logs for anything mentioning a limit being hit or something that might help explain that behaviour (probably for the HTTPListener component).
As a last resort, you might want to do a network trace (Wireshark, NetMon, etc...) with or without the help of your network team. That should help you see what is happening from the network side and might help direct where to look for the issue's root cause next.
Hi! Did you ever find out why you were getting the broken pipe warning? I've seem to have encountered the same problem. One observation from my side is that I'm low on free RAM on the machine, but I don't know if this is related or not.