"L'architetto lasciava la moglie dopo due anni."
Somehow, in colloquial speaking you can at times omit the possessive if it agrees with the person: "Ho lasciato le chiavi a casa" (I left my keys at home), "Dove hai parcheggiato la macchina?" (Where did you park your car?), "Il padre fa l'avvocato" (His/her father is a lawyer), "Sincronizzate gli orologi" (Synchronize your watches) and so on.
I agree, at least in part. Perhaps it's the way Italians think of their wives? "The wife" as we would say = "la moglie" "The architect leaves the wife after two years" would be colloquial English and better said as "The architect leaves his wife after two years" by inference. Your sentence, containing "la sua" would I think be more correctly put as simply "sua" given that the wife is a single near relative. Hope this hasn't just served to confuse!
Besides expressing a continuous action, the Italian imperfect has some other, sometimes colloquial, uses; in this case it's called "imperfetto narrativo", and according to Wikipedia it was trendy between the late 19th and early 20th century to present the chain of past events like a set of pictures. Nowadays it's often used in bureaucratic reports because of the detached feel it gives to the exposition.