Without enabling the "Manage stock" option, the item inventory will not update or sync.
Please be sure to note: if there are only simple products, the SKU should be listed under the inventory tab. However, if there are variable products, the SKU should be input under the variations tab, while the inventory tab should remain empty.
1. If you only have simple products, first login to your WooCommerce Dashboard.
2. Next, click on WooCommerce > settings located in the tabs on the left.
3. In the new window, click on the Products tab, and then click on the Inventory tab.
4. You should see the window pictured above. On the left it will say "Manage Stock" and you should tick the box next to "Enable stock management".
If you have both simple products and variant products, the process will be slightly different.
1. To input the SKU for simple products, first go to the product data page.
2. Make sure the product data is set to "Simple Product"
3. Next go to the inventory tab on the lefthand side. On this page you will be able to input the product SKU and also enable the "manage stock" option at the product level.
1. To do this for variant products, first login to your WooCommerce Dashboard.
2. Next, create your product by clicking Products > Add new product on the left side tab.
3. After setting up the product you desire, scroll down to the data management Box.
4. In the Product Data dropdown, select Variable Product.
5. Now, on the left side tab, set up the attributes for your product. Then, a new tab titled Variations will appear. Click this tab.
6. Once your products are created, you can click on each individual product to see more options. Here, you must input the SKU number for each product. You must also select the Manage Stock option on this page.
Please note that each variant must have its own SKU.
This information and photos were taken from the WooCommerce FAQ page.