We had an issue today (Jul 25th, 2017) of Jenkins running out of file descriptors.
Things already reached the point where Jenkins was barely functioning so to get things back to working order I've:
Manually added a line in '/etc/security/limits.conf' to set 'nofiles' to 16384 for the 'jenkins' user (Previously it was just not configured and seems to have defaulted to 4096).
Restarted the 'jenkins' service.
We now need to:
Place this configuration in Puppet/Ansible.
Add monitoring so we'll know in advance the next time Jenkins goes near to the nofiles limit.