When you sell an item on your Shopify site, the inventory will immediately become committed in Heartland Retail and will be unavailable to sell on the website. However when an item is sold in Heartland Retail, it can take up to an hour for the inventory to be updated on Shopify. This is due to API limits set by Shopify that control how often we are able to send inventory updates.
When you add a new item to Heartland Retail then add that item to Shopify with the Heartland Retail item number matching the SKU field in Shopify. It can take some time for the quantities to initially update on Shopify. This too is due to the API limits set by Shopify.
Related: How to integrate your Shopify webstore with Heartland Retail