This is odd that they deactivated their accounts and seems to be ignoring notes...

By any chance did their T.O.S say anything about lost/damaged items through the mail? There may be a chance that it got shipped out and got lost in the mail.

Ether way the artist SHOULD contact you back no matter what. If you find them/get them to reply back and get them to send the badge (if they did not). If they did and it has not shown up try to ask them if they can make a digital copy of this badge and re send it your way.