If an item with duration '30 days' goes out of stock on source, will it go OOS on my eBay store as well?

When an item's duration is "30 days" it cannot change to OOS neither on HGR nor your eBay store. If you ever want to change it through HGR, you will get an error message directly from eBay. To prevent this, we recommend enabling the "Out of stock action" that increases the item's price when being OOS on supplier. You will find this setting under Settings > Account.