What is the major dramatic question in "Rosencrantz and Guildenstern Are Dead"?

I would say that Fate is the dramatic question if Rosencrantz and Guildenstern are dead, and it is that question that follows and leads the story. Rosencrantz and Guildenstern have to die....

To reply to the other answer, fate is not the premise of the play, the premise is that we choose are own fate, at the end Rosencrantz says, " there was a point, where we could of said no, but I don't remember..." .The point is Hamlet asks three times, were you sent for? They avoid it and then they finally confess that they were sent for. They loose Hamlet's trust right then. Then when their on the boat they could of told Hamlet that he was being sent to England to be killed, but they didn't. In the end they decided their own fate by being " neutral to their will and matter." 

The relationship between the audience and the players is also investigated. I believe that Stoppard is focusing on both the role of fate but also the problem of art. The artist/player/playwright...