You can ask the same question for, well, most wars ever actually in the modern era. How did people continue to get thrown "into the meatgrinder" in WWII? Or in the 30 Years' War? Or Vietnam? Or Korea or the Spanish Civil War?

Ultimately it's for a garden variety of reasons and it depends on who you are speaking with respect to. The general trend can be, frankly, that most people at home did not know the level of casualties being sustained on the fronts and even if they did they were far enough removed from it.

I know I'm dancing around the question here but it's just such a varied and complex question that can and does vary from individual to individual. Quite generally a Serbian or a Frenchman or a Russian can clearly justify their war as defensive (as they are fighting on their own turf) and that garners massive public support; but even then the Russian military system collapsed on itself into revolution after years of struggle. The Ottomans were reclaiming what they perceived as lost territory and defending their borders from British incursion. The Austro-Hungarians, well, public opinion and morale was never really high there so yeah. Germany maintained high public opinion and morale in the early stages of the war because they were flat out winning but considering by the end of Summer 1918 Berlin was in the hands of revolutionaries, every naval base in Europe was in full revolt against the government, and Bavaria was about to secede as a Soviet Republic it's hard to say they managed to keep morale high as well.

What you're likely talking about is the British and that's just a unique case again. Go from 1914 to 1916 and you got people signing up because they want to protect the Empire or for adventure or for whatever other reason. Public opinion was high even despite propaganda because Britain was not personally experiencing the trauma of the war just yet. It would not be until the Somme that Britain would fully commit herself to the war effort and, even despite failures like at Gallipoli, were still an overall boon. Things like the Battle of Mons in 1914, known for the supposed Angel of Mons, played into the British psyche of their superiority as soldiers and their protectors of the oppressed Belgian, etc. Really just a mix of wanting to leave the horrible conditions of home mixed in with a sense of purpose (protecting Belgium from atrocities) and adventure as a whole motivated hundreds of thousands to sign up for Kitchener's New Army.

After conscription took hold in 1916 public opinion did go down but, again, most people were removed from the fighting. We see in retrospect pictures of the trenches and all these accounts but they didn't quite know that back then at the time. Further controversial is the fact that, to be frank, trench conditions and fighting conditions were, for the average brit, really not that uniquely horrible. Ultimately the industrialized, barren trench conditions were comparable to the industrial or industrial mining conditions back on the island; the "commoner" of the British working class often felt right at home in the trenches; we notice that most of these horribly traumatizing depictions of trench conditions come from a distinctly middle class rural tradition of authors who had never experienced those types of conditions before. Just food for thought there.

So really how did Britain convince people it was still a worthy fight? Because they had invested so much. That's what made it total warfare, they were totally involved. Nothing short of total victory would be accepted for the investment put in. No one, especially those fighting in the trenches, would accept anything short of total victory or total defeat considering how much they had personally invested into this conflict; it just was not acceptable to them.

Though I must say that your depiction of "millions upon millions killed each year" to be a bit of an exaggeration; the British lost 522,000-ish men between July 1914 and July 1st 1916 and 2,200,000-ish men from July 1st 1916 to November 11th 1918. In other words an average of ~260,000 casualties a year for the first two years and ~880,000 a year for the second half. That's a tragedy but it's not what you would initially think; "only" 9 million total, across the entire war were casualties of combat. Those numbers were pretty evenly spread around to be honest.

Dammit, I axed the tab I was writing in and lost everything near the end, so this may be a bit shorter this time. You'd think I'd know better by now.

Anyway, in Canada, public opinion and morale did not remain high. Voluntary enlistment had dropped considerably by 1917 as news of what was going on in Europe began to filter home. There was also growing resentment toward Quebec, and to a lesser extent, the Maritimes, for the lower rate of enlistment there. Quebec did not have the strong ties with France that English Canada still did with England (to the point that the only reason that Canada was in the war in the first place was that it couldn't not be--it had no control over its foreign affairs at this point), so the common appeal to fight to defend the "mother country" fell rather flat on French ears. In addition, there was a considerable language barrier faced by francophones, as you had to be able to demonstrate English fluency to enlist. There was only one francophone regiment, the 22nd (better known as the Van Doos). Otherwise, francophone soldiers were broken up and distributed among other regiments. Needless to say, these viewpoints and issues were not well received in English Canada.

Meanwhile, the Borden government was looking at conscription as a means of boosting enlistment. It was a contentious proposal and the 1917 election was largely fought around it. In preparation for that election, the government passed the Military Voters Act and the Wartime Elections Act. The first gave the vote to women who were related to soldiers, the first Canadian women to vote, on the assumption that this group was more likely to vote in favour of conscription. The second act took the vote from those deemed "enemy aliens" on the assumption they would be less likely to vote for conscription. In other words, the Borden government tried quite literally to stack the vote in their favour. The election was hard-fought and bitter, with the English press accusing Quebec of "slacktivism", disloyalty and cowardice and the French returning fire by accusing the government of levying a "blood tax." Nevertheless, Borden's government was returned as the Military Service Act (conscription), took effect on January 1, 1918. 93% of those eligible sought exemptions.

In Quebec, where opposition was fiercest, tensions boiled over on Easter weekend. A man was arrested in Quebec City for not having his conscription enrollment papers on him and riots broke out. They raged all weekend, targeting the military offices and English shops, and threatened to spirl completely out of control. On Easter Monday, the War Measures Act was invoked and mounted troops from Ontario rode in the squelch the violence. By the end, four lay dead and at least 150 injured. Quebec remained occupied until 1919 by some 6000 soldiers, intended to keep the peace and enforce conscription.

So to answer you more directly, after a certain point, conscription was passed and men were forced.