Many shopping carts and marketplace have strict daily limits on the number of API calls (ie the number of times the software such as Finale Inventory can communicate with it).
When the connection is set to "Automatic Mode", Finale is designed to only push stock levels for three scenarios
(1) Finale will update within 5 minutes of a stock change for the specific product
(2) Finale will update within 5 minutes if any of the product's attributes has changed
(3) Once a night, Finale will update ALL product lookups to ensure Finale and the marketplace are in sync
If you want Finale to update skus immediatley, we suggest typically modify the product attribute by populating an unused field and saving the changes.
We typically just add a character such as "=" in the 'product notes' field to trigger a stock update.