I ran into this same problem. Here are the steps I took that make it not work.
1. I searched for the SKU of a variation in a variable product.
2. Just the variation came up in the search results
3. I changed the number under stock.
4. When I clicked out of the field the Save All Changes button appeared.
5. When I clicked on the Save All Changes button the screen went blank with just the WooCommerce Stock Manager header and there were 3 JS errors saying TypeError: “e.images is undefined”
6. I clicked on WooCommerce Stock Manager on the left menu to get back into the tool and the stock for that item was not updated.
7. I then searched for the product by name and the whole variable product came up in the results.
8. I clicked on the Variable product gray box in the Product type column
9. I went to change the stock in the same variation (that did not work when just the variation came up) and saved it and the stock was updated.
So it looks like there is a problem updating a variation when you search for just the variation, but it updates when you have the whole variable product there. I just updated to the latest 2.1.0 and it is acting like this.