The short answer is that they have not technically ever stopped leading from the front.

Of course, it depends on what you're talking about specifically. Leading and engaging in close combat or simply being at the front and capable of coming under fire.

In the sense that they would regularly enter hand to hand or close range combat, this slowly disappeared starting around the time of the U.S. Civil War.

In that conflict, it was already the rough rule that commanders of brigades would still lead from the front with the ranks, while corps commanders and higher would be expected to lead from the rear. Indeed, George Pickett at Gettysburg took something of a hit to his reputation because he didn't die with the rest of his men in the charge named after him, but it has been pointed out that Pickett was the corps commander, and would not only not be expected to lead the charge, it would be considered bad form for him to do so.

At the same time, other leaders at approximately the same rank would still lead their troops directly, especially if they were in the cavalry corps. The cavalry was always the closest to the gentlemanly/aristocratic warrior tradition and so this practice died out last in the cavalry. We could use the example of Custer at Little Bighorn here, although Custer at that time was technically only a Lieutenant Colonel and regimental commander who held a brevet Major General rank from his Civil War service.

Why did this still happen in the Civil War and not afterward? The short answer to that is that the Civil War was the last major war where advances on enemy lines would be done in lines with soldiers in ranks.

At the beginning of the Civil War, and indeed throughout most of it, soldiers were armed with muzzle loading muskets. The classic rifle of the Union side of the war was the 1861 Springfield Rifled Musket, although at the beginning of the war, there were 1840's model smoothbore muskets and even earlier flintlock to percussion cap conversion models from the 1810's which were in use.

These muskets were superior to their 18th Century ancestors in many ways, but still were one shot muzzle loaders. This meant that volleys were still fired in ranks to provide a mass of fire, and these volleys were followed up by a bayonet charge and hand-to-hand combat.

This was the last war with these sorts of charges because the Civil War and afterward had a major change in firearms and tactics. First, weapons like repeating rifles were produced. A repeater like a Henry Rifle, and then a Winchester Repeater would increase the rate of fire considerably. An increase in the rate of fire would mean that defenders would have a huge advantage. Although revolvers existed throughout the war for officers and cavalry, these were short ranged pistols which would not have the same impact on infantry attacks.

This huge advantage was completely brought home by the invention of the machine gun later on. After that point, a straight charge like you would see in the Civil War and earlier would be suicide, and this was amply proven in WWI, but also to some extent in the African and other colonial wars.

So, before and during the Civil War, while a charge on an enemy location was often dangerous, there was a decent chance that you'd actually make it to the defenders to enter hand-to-hand. In those cases a general (usually mounted and with a revolver and saber), would have some survivability and stand a decent chance of being able to exert command and control over their units in the melee and after afterward. Which is not to say that generals were safe, but the risk to reward ratio was considerably better.

After the Civil War, even a general on horseback could be gunned down well before they reached the enemy, and ultimately, the front lines became a zone where actual management of larger units became harder to coordinate on the ground.

Further, since fire from cover and eventually fire and manuver tactics were now required, a general on the front lines no longer could view his unit in one mass and command it effectively. His men were now behind cover, and out of sight. The invention of radio made this not only necessary, but a very viable doctrine, so generals now would want to be were the radios were.

Note, however, that generals even up until almost the present have still been on the front or close to the line of battle. There were many examples of generals in under fire in WWII, a primary example of this being Brig. Gen. Theodore Roosevelt, Jr. on Omaha Beach on D-Day. But it should be pointed out that at that point, Roosevelt leading the troops was denied until he persisted and put his request in writing. It helped, but by that time it showed that the tradition of leading directly into battle was more the exception, rather than the rule.

Others point out generals like Rommel and Patton who were close to the front, but again, neither general was ever far from his radio, and while he was at "the front", actually being committed to an assault would not be something they would do. The danger of being killed at the front from a bomb, artillery strike, strafing from aircraft, or surrounded in a very rapid encirclement was still real, but not as visceral as hand to hand combat.