I'm having a similar issue. When I try to move products to a certain page, the product actually disappears. If you search the inventory, it is still listed on the original page, it is not hidden. I have to change the category for it to appear again. Interestingly enough, it is only when I try to move products to a certain page.
I wonder if it is because the URL of the page is the same as the category name? I am able to move all of my products freely to any other store...just not the one that has the same URL as the category. Thoughts?