From my experience, the main reason for the low number of CS majors is simple: most students don't know what Computer Science is. At the university where I teach, half of the CS majors arrived on campus not knowing they would major in Computer Science simply because they didn't know what CS was. Only after taking a first year engineering sequence where they sample different aspects of multiple engineering disciplines do many of these students realize CS is an attractive and interesting field to study.
Moreover, I have taught a variety of introductory to computing courses to non-CS majors (ie. humanities and business) and what I've found is that a number of students (particularly women) really enjoy the computing classes and say they wish they had majored or minored in CS, but they didn't know what it was until they took the class. A few actually do switch into a computing related major afterwards, though not necessarily CS.
This may seem counter-intuitive, but while many people know how to use computers and technology, many people don't actually understand how it works. Because of this, Computer Science is a mystery to most people and so they don't consider it. This is in part why I am excited about the CS4All movement at the K-12 level... simply exposing Computer Science or computational thinking will go a long way in attracting more people to the major.
Alternatively, another reason why you don't necessarily see a growth in CS majors is because programming is not restricted to Computer Science. Most science and engineering disciplines involve programming now and many curriculums will have programming courses. This is even true in humanities (ie. digital humanities) and business (ie. data analytics) where coding is becoming a desirable skill. If you had a deep interest in say economics and needed to develop some programming skills to simulate models or evaluate data, you can gain these skills and knowledge outside of the CS major and I think that is a good thing.
With this in mind, I think a lot of CS departments will need to consider the shift from being a "destination" major to a "service" major where a significant portion of the teaching load is to non-CS majors who want a minimal core, but not all of CS. A flat growth in CS majors does not necessarily mean a lack of computing or programming education in general.
Finally, I would say that in my department, we have seen record growth in the past few years (from 50 a few years ago to 150) and that is caused a number of problems. This is not restricted to our university as noted in "Generation CS" from CRA:
http://cra.org/data/generation-cs/
So for us, the challenge for us is not growing the number of majors but how to manage the surge in a sustainable manner.