Special character models represent heroic individuals from the Warhammer World, mighty Orc warlords such as Azhag the Slaughterer, emperors and kings, evil lords and famous sorcerers.
It is possible to allow special characters to gain veteran status as described already, but it is unreasonable to 'kill them off' permanently if they are slain in a battle. Whilst an ordinary character model can be renamed and fielded as a new hero or wizard, this isn't the case with special characters, which are often unique models.
Therefore, when a special character is slain in a battle he is assumed to be badly wounded but not killed or destroyed. The character loses all his veteran bonuses and must miss his next game against the same opponent to represent time spent recuperating.
Bear in mind this 'miss one game' penalty for special characters only applies against the same opponent, not against other players in the group. The loss of veteran bonuses, however, is a permanent loss, the character will have to start building up his bonuses from scratch.