@mal2013,
The only answer I can think of is communication, which it sounds like you are already doing.
He has made it clear that he wants the relationship. He has also communicated that things are happening in his life and that he feels pressure. What he feels is just something you have to accept.
You should make sure that he knows how you feel. It is best to express your feelings as your feelings only, don't blame him for how you feel. Your feelings are just things that you have to accept.
My advice is that you tell him exactly what you have said here. Definitely tell him that you are happy when he initiates communication. And tell him that it hurts when you feel he is withdrawing. You also have to let him know where you are in the relationship and if he is reaching a point where he risks losing you... if we love someone we can tolerate a lot of difficulty for them, but there is also a point in any healthy relationship where things will no longer work. You need to communicate this as well.
Then you and he together can focus on things you can do to strengthen the relationship even through a difficult time. Tell him the things that he can do, even while he is feeling this pressure, to reassure you and to make you feel better. Then listen carefully to what he tells you about what he wants and needs whether that is space or reassurance.
As far as whether you should initiate contact more, why not ask him? Tell him that you are feeling uncomfortable and that you need to feel connection with him and let him tell you what he needs. Then you can figure out a way to meet both of your needs.