This sounds like two issues. One, you are triggering a leader election somehow. Do you see session expiration errors in the logs? You may need to raise the timeout.
The second issue is probably related to what came out of https://issues.apache.org/jira/browse/SOLR-3939 Shards that have no versions (because they are empty or just replicated) cannot become the leader. So if your indexes are empty and a leader election is triggered, no one ends up becoming the leader. This will be addressed in a release shortly, but the simple workaround for now is simply to restart the shard and you will get a leader. Next, you want to figure out why a leader election is being triggered at that time (eg a zk session timeout?). Is the system under heavy load at that point? - Mark
