Hey, i had the exact same issue with our AJA Card and FCP7 today…
while veing in communication with the AJA tech support, i tried to solve another issue and found the root of the problem by accident…
Basically what it comes down to is sloppy cabling.
I had a cable in the analog Input 2 of the breakout box that for some reason created a feedback. as soon as i pulled that cable, all the sounds were played back properly.
I told the AJA support my findings, and they were as baffled as me. And agreed with me, that this should not be a reason for this error to occur and they will look into it. But nevertheless, this was the cause.
I fixed the Cables since and everything works fine.
Hope this helps