English Translation
Women automatically lose interest in him after exchanging a couple of words.
Unnatural robotic translation… I would translate the English sentence as
二言、三言交わしただけで、女性たちは彼に興覚めしてしまう。（ふたこと、みことかわしただけで、じょせいたちはかれにきょうざめしてしまう）
軽く言葉を交わしただけで、女性たちは彼への関心を失ってしまう。（かるくことばをかわしただけで、じょせいたちはかれへのかんしんをうしなってしまう）
と as in 交わすと in the original translation is awkward. The conjunction と functions to bridge two actions chronologically, but と doesn’t have the nuance of a “cause-effect” relationship between the two actions.
Translating “automatically” as 自然と is not wrong but makes the whole sentence a bit unnatural. ～だけで (once women did X, ) would be much better.
The subject 女性は is also not accurate. 女性は in this sentence is more likely translated as “the woman” or “a woman” (singular). But the English sentence implies that any women easily lose their interest in him. The original Japanese sentence lacks the nuance of generalization.