AliExpress has recently made changes, so our app can not get the inventory information from there. Besides that, if the customer sets Product Setting as "Set quantity to Zero", then the stock will absolutely updated as Out of stock, and this info will be synced to Shopify as well. Please follow the temporary solution:
In Product Setting => Choose "Do nothing" option instead of "Set quantity to zero", then you should choose the product with the status "out of stock" on Shopify and check in Inventory section, then choose the option "Continue selling when out of stock"
Login to AE on another tab, then use the same link to override that product to update new stock information
Re-Import that product
Meantimes, our technical dev are still checking on it and let you know once we have done
Should you need further support, please feel free to contact us via live chat in-app or email us at firstname.lastname@example.org