Clearly, if you are the boss and pride yourself on projecting a calm and ruthless aura of power, then you should not let rumors of your potential demise or flight proliferate in the wake of civil unrest (or civil war, in the case of Syria). These are warning signs that if unheeded will loosen a tyrant's grip on power and lead to a probably violent end. Once the citizenry can imagine the leader as a cowering, frightened figure -- someone who fears the people as they turn on him -- then a general insurrection is in the cards. Simply put: when they whisper 'where is Assad?', it will be payback time very soon.
It could also be argued that the ultimate cycle of the 'falling dictator' arc begins with a bloody-handed response to legitimate unrest, and the particular ruthlessness of Assad's response to the uprising in Syria would seem to bear this out. In any case, the rumors are starting and perhaps, very soon, another domino will fall as well.