I had the same problem and did something similar, but not exactly the same.
First of all, I have Multistore enabled. So when I was trying to upload new pictures to a new product, I only had the shop corresponding to that product.
So I thought: "Let's try choosing All shops" (I guess that's the name for it, in Spanish is "Todas las tiendas"). After that I tried again and ticked no pictures, saved and ticked all pictures again. I uploaded a new picture and it worked. I then tried to delete old pictures from that product and it also worked.
So it seems to work now. Anyway, I found the following bug: the "Position" for each picture is sometimes duplicated. I guess that's the cause of the problem. Looks like Prestashop messes up with the positions when Multistore is enabled...: