An important incident was the loss of the five Sullivan brothers aboard a single ship in 1942. The incident resulted in a 1944 film and also helped inspire a change in policy.

Apologies for the sparse response, but Saving Private Ryan was apparently inspired by the story of the Niland Brothers. Fritz Niland and two of his three brothers were involved in the D-Day invasions. During a lull in the fighting a few days into the invasion, Fritz attempted to track down his brothers, but discovered that they had both died on D-Day. Around that same time, a chaplain named Francis Sampson tracked him down to tell him that his 3rd brother, a pilot in Burma, had been shot down a few weeks ago and was presumed dead. Fritz was pulled out of Europe and sent back to New York to serve as an MP until the end of the war. As it turned out, his brother Ed (the pilot in Burma) parachuted out of his aircraft and was captured by the Japanese. While he suffered as a POW, he survived the war and lived a long life.

There seems to be some confusion regarding the degree of Sampson's involvement in the matter of Fritz getting sent back home. Band of Brothers says that Sampson was merely telling Fritz about his brother in Burma. Other sources say that Sampson actually knew that all 3 of Fritz's brothers were killed, and was given the task of tracking Fritz down and bringing him to safety. I can't seem to find any mention of who in particular decided to withdraw Fritz from the front line beyond "the Army" or "top brass."

The wikipedia entry has several sources that are worth checking out. The article from Canisius College has pdfs of several contemporary newspaper articles about the event.