I do not believe that cut and pasting a folder from a CF card could cause damage to a card to the point that you would notice,. let alone be unable to recover from it. I'd let that theory go.
For the record, I always copy or cut the folder, or drag and drop. (same as copy and paste) simply because it seems faster than selecting all and then dragging/copying.
Making the folder disappear via cutting it in an OS has zero ill effects. As soon as the card is reinserted, the little red light blinks and bam, you have a new folder.
In practice copying and pasting vs. cut, is more of a safe way to operate. But the possible disasters from cutting would not include the early death of the card.