There could be several reasons a course does not display in a learner's "+ADD A COURSE" search.
First, If a learner is actively enrolled in a training, the training does not display to prevent duplicate enrollments. The best practice for a learner is to review their My Learning - Current tab, which is the default page that displays when a learner logs in. If they don't see the course or event they are looking for, then they should search for the course by selecting "+ADD A COURSE.'
Any administrator can also pull up the learner's blue book and click the "Current" tab to see if there is a current enrollment on that page.
Second, the course might not be "Approved." The administrator should go to Training & Enrollment > Courses & Enrollment and search for the course. If the Approved column does not display a check-mark, that means the course is not approved and cannot be enrolled into. The administrator would need to approve the course for the learner to see it in the "+ADD A COURSE" search.
Third, the course may not have the "Allow learners to self-enroll" box checked off. The administrator should go to Training & Enrollment > Courses & Enrollment and search for the course. Then click the course name and on the Properties tab that displays, go to Step 4 ENROLLMENT SETTINGS and find the "Allow learners to self-enroll." If there is not a check mark, click the check box and then click "Save" to allow learners to locate the course in the "+ADD A COURSE" search.