Luckily my 2nd post is a bit more optimistic
I remembered I had encountered this situation earlier. Back then I didn't think much of it 'cause I was convinced it was caused by an odd placed docking port. I deleted that craft and without knowing it, I had solved the problem 'cause the next dockings all went by the numbers. In retrospective, I'm starting to think there was nothing wrong with the docking port at all but it is caused by a different thing.
I noticed that no matter what I did, the station always kept the target vessel as a target even when I had unset the target. I did the same as I did before, deleted the craft that showed up as target (even unsetting it) and now I can dock again.
As to why this happens, I can only come up with one significant difference in my game play behavior. As I was getting more and more experienced with docking, I started warping closer and closer to the intersection through the 2.2 km barrier (where the game actually loads the ships). Maybe that has something to do with it.
Hope this helps you too.
[EDIT]
I've done some testing, I loaded up the vessel that gave me problems earlier as well as the craft that was the reason for me posting here. Both dock fine without any changes to the crafts. Deleting the vessel (from the tracking station) that refuses to dock certainly resets whatever is going wrong. Not really a cool solution but for me it has worked twice now. At least it is better to lose one craft than to have an entirely useless station floating around.
I have a strong feeling it has to do with warping through the 2.2 km barrier because warping itself has caused problems for me earlier in my game; Warping through a SOI does horrible things for me. Maybe it is unrelated and it is caused by something totally different, but since I started warping closer and closer towards my stations (500m) the problem started to arise.
[EDIT2]
@OP or whoever gets stranded on this page with the same problem:
I've done some more Google-searching and came up with this:
Seems there are more people running into this.