In a situation where R3 scores after R2 is put out for failing to retouch, what is the status of R3's run?

In the described scenario, R3's run counts because it occurred as a result of a timing play. A timing play involves a situation in which a runner scores after the ball is live and in active play, not affecting the previous plays involving other runners. In this case, R2's failure to retouch does not impact R3's ability to score.

The key in this situation is understanding that R3's run is not contingent upon R2's status. Even though R2 was put out for failing to retouch, that does not negate R3's run as it was completed prior to the appeal on R2. Therefore, runs scored on timing plays are valid as long as the scoring runner legally touches home plate.

The other choices relate to misunderstanding the concepts of force plays and the impact of a runner's actions on the scoring of other players. Since R3's situation was classified as a timing play, it stands distinct from any issues that arose with R2, solidifying the legitimacy of R3's run.