Archiving, and why it is better than deleting
Archiving takes a listing out of the directory and keeps everything else; deleting is only for something published by mistake.
Archiving takes a listing out of the directory while keeping its page, its history and its deals intact. Anyone holding a link still sees something sensible rather than a dead end.
It is also how you free capacity: an archived listing stops counting against your plan's active-listing limit, and can be brought back later.
Archive when: the thing is temporarily unavailable, the season is over, or you are replacing it with a better version.
Deleting is for something published by mistake. It is not the way to pause something, and it is not available once deals exist — that history has to stay.