This thread is resolved. Here is a description of the problem and solution.
Problem: When used a domain per language, the top bar is not displayed in the secondary language.
Solution: They are two domains and so are two different cookies. For this reason, a domain appears logged in and another does not.
Unfortunately, at the moment, we do not have a workaround for this. This is on our list of requested features, but we do not have a deadline of when or if this will be added in WPML.
This is the technical support forum for WPML - the multilingual WordPress plugin.