The time it takes to update preorder inventory depends on how you're updating the product in Shopify.
Shopify Inventory Update Methods
How are you updating the inventory?
Are you editing the product via the “Edit Product” screen in Shopify?
If yes, Shopify notifies PreOrder Now (PON) of the change.
Inventory updates in PON may take a few minutes after the change.
Are you using the “Incoming Inventory” or “Receive Inventory” screen?
If yes, Shopify does not notify our servers about this change.
This is a Shopify limitation, not a bug in the PON app.
Workaround for Method #2
If you're using the “Receive Inventory” flow, we recommend using the “Sync Products” link in the app to ensure the inventory reflects correctly in PreOrder Now.