Let's say Lt. Colzet has a target lock on an enemy YT-1300 with facedown damage cards and he discovers through flipping that one is Blinded Pilot and then proceeds every turn to continually flip that damage card face-up (assuming he re-acquires the target lock every turn).

Is there anything in the rules limiting the Rebel player from shuffling his facedown damage cards on the YT-1300 to prevent the Lt. Colzet player from continually choosing the same damage card?

Colzet's ability says "at random," so you actually have to shuffle them around or use dice to decide which one. The Rebel player would have every right to mix them around, as well.

Bingo!

Let's say Lt. Colzet has a target lock on an enemy YT-1300 with facedown damage cards and he discovers through flipping that one is Blinded Pilot and then proceeds every turn to continually flip that damage card face-up (assuming he re-acquires the target lock every turn).

Is there anything in the rules limiting the Rebel player from shuffling his facedown damage cards on the YT-1300 to prevent the Lt. Colzet player from continually choosing the same damage card?

Nope!

Well, first of all on basic conditions cards facup are not flipped back facedown.

so if you randomly flipped a card faceup it remains faceup.

Well, first of all on basic conditions cards facup are not flipped back facedown.

so if you randomly flipped a card faceup it remains faceup.

Blinded Pilot takes away your attack. Instead of shooting, you flip it face down (even if you wouldn't have actually had an attack).

Yep. Its possible to get the same card, but it must be chosen at random.

A face-down card is completely unknown. While you could learn which cards are on a ship the exact identity of any face-down one of them is unknown until it is turned face-up.

If the Falcon had Munition's Failure and Minor Explosion on it face-down if you are told to turn a card face-up you have a 50:50 chance of picking either on. There is nothing that would let you automatically pick the Minor Explosion to turn face up each time you could flip a card.