During Cold War days, NORAD was blind on more than one occasion for at least more than a few minutes. Titan missile silos were non-operational and nuclear submarines were often outside of radio frequency range. Did the world come to an end? Did we call the Russians on the red phone and say "Hold up, we need a few minutes to get our act back together"?
No. The enemy had no idea that our systems were down for a spell and we had no intention of letting them know. They were too scared of M.A.D. to attempt to attack us when they 'knew' that our systems were always up. I'm sure that the roles were reversed countless times with the Soviet systems being down as well.
The point to my story: Since the enemy is expecting our systems to be up at all times, it is more harmful to admit that the computers are down and create a scene than it is to simply act like the systems are up and take the off chance that a terror group will attempt to illegally enter while the systems are being brought back up and people are simply processed without the border checks.
Telling the world that our computer systems for border control can go down on a whim or be compromised by hackers is really not a smart concept to me.