If the product itself is hidden, resides in a hidden category, or is assigned to a manufacturer that is hidden, then the product will not return in a search.
Go to Inventory >> Manufacturer Manager to check if the manufacturer that product is associated with is not hidden.
Go to Inventory >> Category Manager to check if the category that product is associated with is not hidden.
Go to Inventory >> Product Manager Search for that product. Within the General Tab, ensure that the Hide box is not selected.