In Act III, scenes iii and iv of Romeo and Juliet, why is Romeo considered the protagonist?
The protagonist is essentially defined as the main character of a text, typically the character whose life or progress is followed and is presented with some kind of conflict. For this reason, it would be appropriate to define both Romeo and Juliet as the protagonists of this play. In the first scene you cite, 3.iii, it is easy to see Romeo as a protagonist because it shows Romeo in Friar Lawrence's cell, receiving the news that he has been banished from Verona for murdering Juliet's cousin, Tybalt. We see Romeo's response to his punishment as well as his response to the nurse's news of Juliet's grief. The plan is laid for Romeo to journey to Mantua after spending this one night with his beloved. The entirety of the scene really focuses on Romeo's emotional responses and plans for the future.
However, the next scene, 3.iv, doesn't feature Romeo at all. This scene shows Lord and Lady Capulet discussing marriage plans with Count Paris (who still wants to marry Juliet). It's a very short scene in which they make plans for Juliet's upcoming wedding. However, just because neither Romeo nor Juliet show up in person in this scene doesn't mean that they are no longer the protagonists of the play. In this scene, plans are being made which will very seriously impact their hopes for the future and lead to Juliet's faking her own death (and everything that follows). Therefore, they remain the protagonists even though they aren't in the scene themselves.