That's a good point WholeEnchelada re the being reluctant to invite friends out due to having been refused often due to them always being busy. I come up against that as well and expressing sadness that we'll lose touch if we don't see each other face to face doesn't work. So if issuing a couple of invitations and suggesting dates is met with can't do it and me saying you tell me what suits doesn't get anywhere I just say "I woild really like to meet up with you but it sounds a busy time at the moment so how about you contact me when you do have some time to catch up. Most nights and weekends are good for me but not during the day Mon to Friday" to keep the door open and then I don't continue to make the effort to suggest meet ups for self protection.
So to avoid hurt I don't initiate get togethers much unless I'm confident of getting a yes.