ERROR - Couldn't accept new TLS connection: Too many open files

Perhaps related to my recent upgrade of PMS to the latest:

Apr 26, 2016 19:47:28 [0x7f1cb83fe700] INFO - Plex Media Server v0.9.16.4.1911-ee6e505 - ubuntu PC x86_64 - build: linux-ubuntu-x86_64 ubuntu
Apr 26, 2016 19:47:28 [0x7f1cb83fe700] INFO - Linux version: 3.13.0-37-generic (#64-Ubuntu SMP Mon Sep 22 21:28:38 UTC 2014)
Apr 26, 2016 19:47:28 [0x7f1cb83fe700] INFO - Processor         Intel(R) Core(TM) i7-2600 CPU @ 3.40GHz

I'm out of file descriptors evidently and Plex is unusable (unresponsive to any requests to the server). Let me know what else you might need to help. Attaching the compressed PMS log. Below are some symptoms.

brett@blur /var/lib/plexmediaserver/Library/Application Support/Plex Media Server/Logs $ tail "Plex Media Server.1.log"
Apr 28, 2016 20:27:52 [0x7f1cb6bff700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb63fe700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb6bff700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb63fe700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb6bff700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb63fe700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb6bff700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb63fe700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb6bff700] ERROR - Couldn't accept new TLS connection: Too many open files
Apr 28, 2016 20:27:52 [0x7f1cb63fe700] ERROR - Couldn't accept new TLS connection: Too many open files

brett@blur /var/lib/plexmediaserver/Library/Application Support/Plex Media Server/Logs $ sudo lsof|grep '^Plex'|tail
COMMAND     PID   TID             USER   FD      TYPE             DEVICE  SIZE/OFF       NODE NAME
Plex       1951 31459             plex 1014u     sock                0,7       0t0    9632788 can't identify protocol
Plex       1951 31459             plex 1015u     sock                0,7       0t0    9632790 can't identify protocol
Plex       1951 31459             plex 1016u     sock                0,7       0t0    9632795 can't identify protocol
Plex       1951 31459             plex 1017u     sock                0,7       0t0    9632821 can't identify protocol
Plex       1951 31459             plex 1018u     sock                0,7       0t0    9632823 can't identify protocol
Plex       1951 31459             plex 1019u     sock                0,7       0t0    9632825 can't identify protocol
Plex       1951 31459             plex 1020u     sock                0,7       0t0    9632826 can't identify protocol
Plex       1951 31459             plex 1021u     sock                0,7       0t0    9632827 can't identify protocol
Plex       1951 31459             plex 1022u     sock                0,7       0t0    9632837 can't identify protocol
Plex       1951 31459             plex 1023u     sock                0,7       0t0    9632841 can't identify protocol

brett@blur /var/lib/plexmediaserver/Library/Application Support/Plex Media Server/Logs $ sudo lsof|grep plex|wc -l
80149