This can happen if there are too many open connections.
Try increasing the maxClientCnxns setting.
From documentation:
maxClientCnxns (No Java system property)
Limits the number of concurrent connections (at the socket level) that a single client, identified by IP address, may make to a single member of the ZooKeeper ensemble. This is used to prevent certain classes of DoS attacks, including file descriptor exhaustion. Setting this to 0 or omitting it entirely removes the limit on concurrent connections.
You can edit settings in the config file. Most likely it can be found at /etc/zookeeper/conf/zoo.cfg.
In modern ZooKeeper versions default value is 60. You can increase it by adding the maxClientCnxns=4096 line to the end of the config file.