No, this isn't a trick question. There's a definite end to their arguing in the book. And you may be surprised at the answer.
When John comes to declare his love for Margaret the morning after the riot, the tense relationship between the master and the Milton newcomer reaches a blistering vocal climax. Pent-up emotions on each side explode into forceful words and both are left stunned by the unexpected vehemence of their exchange.
After this staggering tempest, the dynamic between these two strong-minded individuals is forever changed. After this day, Margaret never again raises her voice to argue against him. In fact, the very next day she finds herself defending Thornton to a grieving and bitter Higgins.
The end of the verbal battles between Thornton and Margaret comes precisely at the half-way point of the book. The remaining two hundred pages of the story reveals a softer, meeker Margaret in relation to Thornton. She is jolted into taking a closer look at the man behind the master's mask.
But wait, isn't there still bristling friction between these two passionate people throughout the second half? Yes, of course. But it no longer stems from any perceived ideological or character differences. Outbursts in this portion of the drama erupt not from an indignant Margaret but from an emotionally tortured Thornton, who simply cannot control his bitter jealousy.
The potent tension between Thornton and Margaret after the failed proposal is the result of repressed passions and the accumulation of misunderstandings. The unfortunate havoc wrought by Frederick's appearance convinces Thornton that Margaret loves another and causes Margaret to believe Thornton could never love a confirmed liar. The mistaken belief that they are despised by the other costs both of them almost two years of unnecessary suffering.
This is wholly romantic tension, which has nothing to do with socio-economic conflicting opinions. And it is not resolved until those final pages (or the illustrious train station scene), when their pathetic illusions dissolve in the glorious light of reality.
The very last page has playful arguing between the lovers -- perfect.