A common issue is when you are working in an exhibit site and go to add a recently added item to your page but it isn't showing up in the item set assigned to that exhibit site. While a good explanation for this is lacking, it tends to occur when Items are being added to an Item Set at different stages. This can be resolved by re-adding the Item Set in the Resources section of the Site.
Below is screenshot of this procedure. Please note, you will need to select the "Manage current items" section will need to be placed to "Add - keep existing items and assign items from a new search." The number of items assigned to the site listed at the top should increase after saving. If you have added a lot of new items, it may take a little time for these to be updated.