Have you considered getting married? Just a question. He could apply for a change of conditions to his work visa to make it a visitor's visa. If approved, he can also apply to extend it when it is close to expiring. You also have the option of applying inland (after you complete 12 consecutive months of living together) if he chooses to change to a visitor and then IF you receive Approval In Principle at around the 5 to 6 month mark, he can then apply for an open work permit. Conjugal is a difficult category so expect bumps in the road. Consecutive means just that and there aren't exceptions. IMHO, the breaks you described are too long for you to be considered common-law at this point.
Thanks for your feedback - I was pretty sure those breaks would be considered too long for common-law. Do you think the fact that we have so many short periods living together with breaks in between helps or impedes our case for conjugal? Some periods were in Canada and others in Argentina. The time he spent in Canada was under at first a student visa, and then a temporary work visa. Thanks again!