I have seen this happen several times for several months before now, but this is the first time I've seen it and also got a save that reproduces it all the time. This occurrence is in a new game without mods using the 3.8 opt-in.
The strange behavior occurs when an AI ship or fleet of ships tries to leave a planet. I think it only happens when the ship or fleet is trying to leave a planet that was recently conquered. That is what is happening in this case.
The Snathi and I (Arcean) are at war with the Drath. The Snathi took one of two planets in the star system Engelbrekt, and I took the other. I noticed the Snathi fleet trying to leave the planet they conquered and go towards some other planets, probably to conquer them. The problem kept recurring every turn.
The fleet would leave the planet, move 2 tiles to the SW, vanish and reappear stationed at the planet it just left. When I saved the game the fleet was ejecting from the planet to the NW, moving back to the planet, moving 2 tiles to the SW, vanishing and reappearing back at the planet. I exited the game, restarted, loaded the save and had it happened again. I tried this several times with the same result, so I know it is reproducible.
Here is a screenshot showing the Arcean home system and the star system where it is happening.
How to Reproduce
Start GalCiv3 with the 3.8 opt-in, then load the save "3.8 Opt-In Strange Ship Behavior".
You will be at the Arcean home system. Zoom out, then move to the left and down a little to find the star system Engelbrekt. One planet will be Arcean, and the other will be Snathi. The problem is at the Snathi planet.
The save was made so that all you need to do is click on Turn. The Snathi fleet will probably eject from the planet to the NW, move back to the planet but still be visible, move 2 tiles to the SW of the planet, vanish, then be back at the planet. If you want to, you can play another turn, and it will happen again. It will probably keep happening for as many turns as it takes until something changes and it stops happening. I have no idea what that change may be.
The save is available here.