SYMPTOM:
When when elements listed are identical, some prompts do not give you a search box below the list of available attribute elements in Strategy Developer and Web 9.x and 10.x:

Below is an example of the prompt screen with the search box.

CAUSE:
This is working as designed. The prompt created with pre-defined list will not come with the search box option.

Same behavior can be seen in Strategy Web with some prompt styles.
ACTION:
If search box is required, select other than "Use a pre-defined list of elements" when creating an attribute element prompt.