try to review the access log for connection events related to those from the errors log file mentioned earlier, and also verify on the remote replica, the errors and access log events corresponding to this connection, as well as file descriptors and LDAP thread use, run some netstat and dsconf monitor commands:
dsconf SOME-INSTANCE-NAME-HERE config get nsslapd-conntablesize nsslapd-threadnumber nsslapd-maxdescriptors
dsconf SOME-INSTANCE-NAME-HERE monitor server
sysctl net.core.somaxconn net.ipv4.tcp_max_syn_backlog