Personally, I don't see how a LDR can ever be worthwhile with a person who does not appear to have much time for an IPR (In-person Relationship).
I know your heart may be invested in him/her, but I also think you deserve more than you can possibly get out of this relationship as it exists.
If I were in your shoes, I'd cut my losses and move on. If the two of you are meant to be, it will work itself out when the timing is right for both of you.
Every good relationship needs balance. While they are almost never perfectly balanced, in that one person will usually have to put forth slightly more effort than the other from time to time, the one you describe appears to only have you putting forth any effort at all. That isn't a relationship. Depending on the level of effort you put forth, it may be stalking.
I've been where you now are. It sucks to want someone more than they want you, but there is nothing healthy for you to do except move on. The sooner you do, the sooner you may find happiness. Closing the door on this relationship, or attempted relationship, may open more doors to other relationships.
Just remember: You can never get a refund for your time, so never let anyone waste it.