Is a unit ever required to test morale more than once in a given Morale phase?
No. To clarify how this works, each unit that has morale markers on it at the beginning of the Morale phase will test morale once. The order of testing is not important since all testing is considered simultaneous. If a breaking unit places more morale markers on the table during the phase (for seeing retiring friends), those markers are not counted in the current phase and will be held over until the next Morale phase.