They are. So it is not going to move at all. I tried time warping a couple of years just in case, but as far as I can tell, it didn't move a single degree.
It is not just a synchronous orbit, it is a stationary orbit, so I need to be above a specific point on the surface (the waypoint marker on Duna). But that particular spot in the sky is occupied by the moon. If I get close to that orbit/longitude, I get captured by Ike's gravity, and I'm no longer in the designated orbit.