I've had this issue for some time and seen others with it as well. You create a reading plan, and it shows up immediately on your device - in my case iPad or iPhone. You do some reading on your device - and it says you are up to date, but your computer does not.....
I also noticed quite a few other people posted a similar problem. So I did some testing.
For me the resolution was to allow Logos to see my location.... I am pretty strict where it comes to allowing location services and saw no reason for Logos to need it. But the moment i enabled location services - my reading plans now sync.
Hopefully this helps you out, and maybe someone can pass to the developers to set it so it's not needed to have location services to sync reading plan progress?