Question was cross-posted at http://stackoverflow.com/questions/35360782/nuxeo-cluster-load-balancer-session-replication-failed/35362138#35362138. Here is the answer:

That is expected: the session is sticky, not replicated. As stated in the documentation, you will have to authenticate again or not, depending on your configuration and architecture:

The Nuxeo Platform requires all calls to be authenticated. Depending on your architecture, authentication can be stateless (ex: Basic Auth) or stateful (ex: Form + Cookie). Either way, you probably don't want to replay authentication during all calls.

That's why having a session based authentication + session affinity can make sense: you don't have to re-authenticate each time you call the server.

If the session affinity can not be restored, for example because the target server has been shutdown:

• stateless authentication will be automatically replayed (ex: Basic Auth)
• for stateful authentication:

•    if you have a SSO this will be transparent
  

•    if you don't have a SSO, user will have to authenticate again.
  

Seems like Nuxeo is not (yet) able to manipulate server.xml of Tomcat to add clustering properties. (please, correct me if I'm wrong). Maybe you can try modifiyng server.xml.nxftl adding some extra properties and then setting values in nuxeo.conf. In the meanwhile, take a look at https://tomcat.apache.org/tomcat-7.0-doc/cluster-howto.html

Session replication is not very difficult in Tomcat servers. Good luck and come back if you find any solution.