I am experiencing the same thing. I usually do not get many views, but I have a customer base that checks my little shop out more or less frequently. Now I am getting many more views (unusual for my shop), and all of the views, except maybe two or three per day, are coming from direct traffic??? I have noticed that the direct traffic views are for items that I already sold long ago. Very strange.
I am dismayed because I noticed that my regular flow of viewers has disappeared completely, the searches are not there any more, it's just that "direct traffic" that I mentioned before that is looking at already sold items. This is definitely interfering with my regular traffic. From the posts above, it seems there is nothing I can do. I have three shops. Two of them are on vacation right now (for revamping, SEO, new photos, etc.), so this is the only shop that was doing some business - small - but steady. Now it has come to a complete halt.
I wonder if it is even worth it to go to all the trouble and work to revamp my other two shops and open them just to go through the same thing that is happening here. I am really upset about this situation.