As far as I know, saying “your taking time” is technically the correct version, but you will hear “you taking time” plenty often from native speakers. Just try googling “appreciate your doing” and then “appreciate you doing” and see which one has more results. Of course, Google search results aren’t the ultimate authority for grammar issues, but the very first result I got with the “you” version was from the White House website.
I think the difference is purely and simply a question of emphasis. In other words ‘you’ taking the time is ‘you’ and nobody else doing it and ‘your’ taking the time refers to the action of ‘taking the time’.