User Activity

I have some unpaid for items that need to be relisted. However, I do not want the last non paying bidder be able to bid again. Can this person be blocked?
I have to relist my item due to a non-paying customer who won 2 items from me and then said his child did and doesn't want to pay for the winning items. So I would like to block them all together from bidding on my items, is this possible?