Combo products get their availability from the products they are based on. So if e.g. a Horse Riding trip, that is a base product in your combo product is sold out the combo product is sold out.
You have one option to manage the availability for you combo product, by closing days. E.g. maybe you don't want your combo activity to be available in September Then you can close September, even thought both of the base products are still available from the respective vendors.
To close days select the "Product info" tab at the top of the product page.
At the bottom of the product page you have a calendar, where you can see closed days after you add closures. To add a closure select "Add" by closures.
Select the dates that the combo products should be closed.