Here's a simple method to replicate, that seems to always work on my system at least.

1. As a Zeus Game Master, type in random gibberish to the search bar, while in either "Units" or "Groups" tab.
2. Repetitively cycle between the two previously mentioned tabs a couple of times and while doing this the faction icons in both start to disappear one by one until there's none left in either.
3. Clear the search bar and cycle between the tabs once more and only the BLUFOR icon reappears in both whereas all the others are gone for good until the mission is restarted.