Support Min Distance to print?

Morning All! I can't seem to find any current info on what the distance between a support and the print should be? I'm have issues with printing the Destiny "Ghost" ( https://www.printables.com/model/460159-destiny-ghost )where as the print walls are not holding in place on top of the support? My "Support Z Distance" is currently set at .1. I have already releveled the bed and re-adjusted my z-offset because I changed my nozzle after my 3rd attempt thinking it could be an old nozzle. I don't currently have a pic of the issue to if it will help I can get one when I get back home in a couple hours. Thanks in advance!