I think that one of the most meaningful ways in which Sophocles maintains the audience's interest is through the development of Oedipus. As a main character, Oedipus holds the audience's attention. When he enters, confronting the crisis in Thebes, his characterization initiates and sustains the attention of the audience because he goes "all in:" "Then once more I must bring what is dark to light." Oedipus has no problem and no hesitation in declaring that he will embody the force of truth and the ability to make right that which is wrong. Given the challenges that are placed on Oedipus in terms of fate and predestination, his own desire to exact his free will to counteract this becomes an issue of interest to the audience. Sophocles is able to construct both sides in such a manner. The fundamental reason why Oedipus' characterization sustains the interest of the audience is simply to see if he will be able to make good on his promise.
This becomes Sophocles' central point in being able to maintain the audience's attention. As the audience watches how Oedipus will navigate the demands of fate as well as his own commitment to exposing the truth, their interest is both piqued and maintained. There is a clear desire for the audience to see how this collision will be balanced. In this, Sophocles is able to maintain the audience's attention until the end of the drama with a conclusion that embodies the essence of dramatic tension.