Then why the need to enact conscription in 1862 and forcibly extend all enlistments for the duration of the war? Something Lincoln never dreamed of doing?
The problem retaining troops was not the mission, rather for the South the problem with troop retention was just being in the Confederate Army because it was so arduous, feast or famine food, maybe decent uniforms maybe not, and strict disciplinarian generals that loved to fight but cared little about the day to day running of armies.
So they were willing to fight but not willing to put up with hardships? Really? I imagine if faced with a Valley Forge the Confederate army would have deserted on day one, huh?
The problem for the North was the war was not really popular.
And yet the Union army remained overwhelmingly powerful throughout the war. The army could have faded away in the spring and summer of 1864 when the three year enlistments ran out. It didn't because the overwhelming majority of the troops reenlisted to see the war through to its successful conclusion.
Having four times the population and having the war fought in other people's land gives you quite an advantage in that regard.