With Starlink your link is dependant on two issues: 1) can your terminal see a satellite and 2) can the satellite get to an earth based down station.
When Starlink add down stations they will often steer their customers to use satellites “closer” to the down station. This is probably why your dish has moved. If there is a new ground station on line then you are getting moved so as to use satellites that can use it.
One of the other main issues for Starlink is that they have to be careful not to interfere with existing satellite services which all tend to be in geostationary orbits and so satellites have to stop transmitting to down stations when they run the risk of interfering.
So you may see all those satellites on a globe and assume you will be able to use any that are in sight but it is not like that only some will be available for you at a particular location on the earth and the position of a suitable ground station is also very important as to which you can use.
There is a plan to add higher level satellites using optical links (which won’t interfere with existing geostationary satellites) this will improve the situation and allow each satellite more access to ground stations as there will be a backbone above them to give new ways to get to a ground stations without interfering.
It’s all described in the FCC filing made by SpaceX a quick search will get you a lot more details!
Happy satellite hunting!
I’m touring in France and moving every day or couple of days… dishy, as we travel further North through France has moved from pointing N (when in southern Spain) to NW. my guess is it’s satellite density and their orbit driving this.