Randy was last seen hiking with his grandfather and two brothers in Peppersauce Canyon in the Santa Catalina Mountains near Oracle, Arizona on April 7, 1979. He wandered ahead of the rest of the group and has never been seen again. An extensive search of the canyon area did not produce any evidence as to Randy's whereabouts. One of the searchers was able to follow the child's footprints to a dirt road, where they stopped; Randy may have gotten into a vehicle at that spot.

In 1985, a woman reported that she had found a dollar bill with the phrase, "I'm alive in Phoenix, Ariz. Help me. Randy Parscale" written on it. Police investigation of this lead turned up no evidence. Investigators are uncertain what happened to Randy. His case is classified as a non-family abduction, but he may have simply become lost in the mountains or fallen down a mine shaft. Randy was a third-grader at Roberts Elementary School in 1979. His case remains unsolved.