[CentOS] performance problems with OpenLDAP and multiple simultaneous clients

Running CentOS7, with openldap-2.4.40-13.el7. The environment consists
of two ldap providers, in mirror mode, serving over a shared virtual IP.
Client-facing services are provided by 4 consumers, most of which are
accessed over a layer 4 load balancer.

Periodically, the consumers encounter some sort of client request(s)
which consume all available threads, cause backload threads to spike,
and cause slapd to go unresponsive for a long period of time. I've no
idea what is causing these events, or if there is anything in the
configurations that I can tweak to help.

Anyone have any ideas?