Welcome to the forum!
I could make a couple of guesses. That tool doesn't get a lot of attention from developers, as far as I can tell. There have even been discussions about dropping it. Although personally, I think if it was working properly, could only benefit Inkscape!
It could be a bug with the tool itself. Or it could be related to a different bug.
Oh wow yeah, I can reproduce that in the simplest of files. And those paths don't behave properly either. For example, I made some shapes and dragged out a connector that curves 90 degrees. If I flip 90 degrees, it flips. If I flip 90 again, instead of flipping in the same direction, it goes back to where it started.
Even though these connector lines are called Paths, I've been able to avoid that flipping behavior by using Object menu > Object to Path. It doesn't do anything obvious to the path, but it changes completely in the XML.
I would suggest trying this. Just before you close a file, do Ctrl A (select all), and then Path menu > Object to Path. Once they are converted to that kind of path, they should not change when you open the file the next time. However, they will no longer behave as a connector. So you won't be able to use the Connector tool to edit them anymore.
I wish I had a better answer for you. Maybe someone else will have an idea? But I'll check the bug tracker, and if these bugs aren't listed already, I'll make sure they are reported.
