It's conceiveable that a car which passes tech before a race or qualifying run would not pass tech after. For example, (and I believe this has been done) a bolt could be installed to keep ride height up to pass tech which is designed to fail on the track lowering the car to an illegal level. Or any other iteration of the same.
Well that's true. It's also the kind of thing the tech people are supposed to be looking for. Maybe if bolts for certain parts were a specific grade that might help. In the case you presented, I would say it was a part failure and disallow the time. I see no reason for fines and suspensions. In Evernhams case there were apparantly some holes in the fender well, which is something not mentioned anywhere in the rules. NASCAR told him to tape over the holes, which he did. During qualifying the tape fell off, as hard as that is to believe. ::) So NASCAR fines Evernham, IMO, for doing what he was told to do by the officials. This brings up another point. If you are smarter than the rules makers and find something not addressed in the rules that gives a little edge, is that cheating or innovation? It seems F-1's opinion is "The boy is smart, we'll allow it for now".
I remember Bobby Allison's rear bumper falling off in the 1982 Daytona race. It was deemed improperly positioned before the race and the crew supposedly did a rush job relocating it. Without a rear bumper Allison's car had less drag and ran away from the field, but no fines or suspensions were levied. Gary Nelson, who is now one of the heads of NASCAR's inspection crew, was Allison's crew chief.