We have a 5 node cluster running 3.4.10 we saw this in .8 and .9 as well), and sometimes, a node gets a read timeout, drops all the connections and tries to re-establish itself to the quorum. It can usually do this in a few seconds, but last night it took almost 15 minutes to reconnect.
These are 5 servers in AWS, and we've tried tuning the timeouts, but the are exceeding any reasonable timeout and still failing.
In the attached logs, 5 is a follower, 3 is the leader. 5 loses connectivity at 11:21:34. 3 sees the disconnect at the same moment.
5 tries to re-establish the quorum, but cannot do it until the connections to the other servers expire at 11:37:02. After the connections are re-established, 5 connects immediately.
At 11:41:08, the operator restarted the server, and it reconnected normally.
I suspect there is a problem with stale connections to the rest of the quorum - the other services on this box were fine (monitoring, puppet) and able to establish new connections with no problems.
I posed this problem to the zookeeper-users list and was asked to open a ticket.