Glenn:
In 1992 Tom Scherrer lost the US Am to Justin Leonard 9 & 8, and the finalists in the Am are invited to The Masters. Scherrer decides to turn pro before the 1993 Masters, thereby relinquishing his invitation (the invitation only applies if they remain an amateur). I asked him about it in a bar one night, and he figured he'd be playing in The Masters regularly before long. He eventually got into the 2001 field, but I think that's it.
(I've got another buddy that turned down an automatic invite to the Masters. He was selected to the Walker Cup team back in '79. Back then, the Walker Cup team was invited to The Masters in even numbered years. But it conflicted with the NCAA Championship. He decided to play in the NCAA, which they won (Ohio State)). Never got back to Augusta.)