It's for more than just hunting parties. I can't tell when it happens, but it happens pretty constantly though randomly.
I've also found that if you have more than 1 unit in a stack that turns invisible, if you send a guy out, he will be visible. Then you can merge the invisible guy into the new army and it will remain visible.
Or yes, saving and reloading.
It seems to have no gameplay impact - just visual bug.
What happened to me that my invisible unit got attacked and I sort of got a battle initiation screen but I couldn't start the battle or retreat. The options were not there. so the unit stayed invisible, the battle map with the deployments zones were drawn on the map but no units or battle options visible. It was like everybody disappeared :) I had to reload eventually. Just "end Turn" did not solve the problem.
This happened to me as well when i accidently clicked on an enemy unit, initiated combat, but instantly spamclicked away. It was mere milliseconds that the combat preview screen popped up before my Units turned around and moved a tile back. That Unitstack was than invisible till i either moved them next turn or initiated combat (sorry can't remember exactly).
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