Why does Cassio lose his position with Othello?
Ambiguous question... But perhaps it's just me, I read this question as; Cassio loosing his position as Lieutenant, Othello's right hand man, thus loses his position with Othello.
'Reputation... I have lost the immortal part of myself." quote Cassio.
Othello dismisses Cassio for drunkenly behaviour; disobeying his orders.
Cassio looses his position with Othello when he (Cassio) tells Iago that he had mentioned Desdimona's unfaithfullness. At that time Emilia (Desdimona's lady-in-waiting) mentions that she had fiefound the handkerchief and had given it to Iago. This causes Othello to realize that Cassio never had the handkerchief at all and that he had killed an innocent person, his wife. He eventually describes Iago as a man with a cloven hoof, the devil.