Hi,
You might have to check the advanced search page you want the "Due By" to be on. And verify if the "Due By" field is in the structure used for the search criteria context node. If it is not there, it is not supported by standard. And whether it is not supported by standard or not is responsible by the bsp component. For example, if the advanced search is AI* component, it should be solution manager topic.
Regarding the "Search and result" option, when we activate it in enhancement, it will trigger extra structure and coding generation, thus there is no such option designed for standard fields.
Hongyan