I believe if they say they've been busy, you aren't important, iin?
I know that I only really ever use the excuse "busy" if the person isn't all that important to me. In other words I make time for people that are important .
I don't brush them off and say sorry didn't keep in touch with you or ignored all your messages because I have been busy. Busy is just a pitiful and cowardly excuse saying you're not important enough for me to make time for you. IIN?