Desdemona intervenes on Cassio's behalf because she knows he is a true friend to her and Othello, as well as a loyal soldier to his general. Cassio played an important role in her and Othello's relationship and ultimate marriage.
Cassio believed in Desdemona's love for Othello and that Othello would be a good husband to her. Cassio played an intermediary role in helping smooth the way with her father.
Although Cassio lost his job after just one episode of drinking, Desdemona knows that Othello will resist changing his mind. One reason is that as a military commander, he is used to making decisions quickly and sticking to them. Changing his mind could undermine his authority and make him seem weak. Othello also has high standards and is unforgiving of others' foibles.