Well since the LDAP replica server wouldn't be running the mailbox service which handles SOAP requests, it makes sense that it gets a connection refused error...
The question remains though if you are getting "the expected results" on the main server how in the world is it not showing as online?!? The admin UI simply runs that SOAP request and then parses the output into the page.
Hmmm.... just had a thought. Is the date/time returned by this recent?
Code:
date -d @`zmsoap -z GetServiceStatusRequest | grep status | head -n1 | cut -f2 -d"\""`