Problems after inventory updates

We have been struggling for some time with random products not displaying in our store after updating inventory quantities. Initially it seemed to happen when inventory was sold down to zero and when the updated quantity was added (via MySync with Quickbooks, the product would not display. The workaround was to ‘Hide’ and then unhide the product. However, this only seemed to work with Simple Products.
The problem seems further complicated with variable products and the Manage Stock function.
We load our product details (description, SKU etc) in WC and then update the inventory quantity through Quickbooks which we have been advised is best practice. Manage Stock is unchecked at parent level but checked at variation level. Our quantities sync perfectly from Quickbooks in that, at variation level, the quantities reflect correctly. BUT in our Product List, it shows the product Out of Stock with zero quantity and hence will not display the product). If we then uncheck Manage Stock at variation level, it then removes the inventory quantity and shows it as In Stock and the product then displays. We then have to go back to the variation and re-check Manage Stock and manually input the inventory quantity. The product still displays.
This is a lot of time-consuming workarounds to get our products to display and reflect stock levels accurately. Can anyone suggest how we solve this for both the simple and variable products?