Up until 1813, with an exception of actions in Spain, the French army had very limited experience in mass desertion. The men of the French army are in a very different army than their enemies, which often use extreme discipline for minor actions. The nature of the French Army and the nature of Napoleons careful cultivation of image helps to create something else.

First, let's discuss the nature of the army and how it differed from the enemy. The greatest benefit a French soldier had was that of the possibility of advancement. In most European armies at the time, officers ranks were only open to the nobility or practically only open to them due to the purchasing of ranks. As soldiers aren't paid well, as well as the fact that most uniform costs after the initial uniform assignment were on the soldier, a nco would have little chance to save to buy a higher rank. The French army disposed of this in the early days of the Revolution and was not revisited during Napoleons reign. As a result, the French army became a very meritocratic and diverse force, with the sons of coopers (Murat) and minor nobility (Davout, Berthier) serving side by side. Further, promotion was done not through absolute favoritism but by suggestion on competence and bravery, although the latter would cause such a loss in middle leadership (colonels and brigades generals) that there would be a brain drain from legitimate loss in combat.

Next, the French army was far less focused on corporal punishment, again a hold over from the Revolution. Rather than shipping soldiers for any minor offense (as it was reserved for only the worst things, such as thief from other soldiers or cowardice in battle), they would often serve in penal units or have time in a battalion prison doing work.

However on the other side, Napoleon brought two things that helped keep soldiers in the army, victory and a personal touch.

Napoleon had a special relationship with his soldiers. With a charisma of 20 and a diplomacy modifier that would make a bard jealous, he made every soldier feel special. Often he would inspect soldiers, see one and reply "you fought with me at Lodi, how are you?" He was able to recognize ancient faces in crowds, greet them and then leave them with a reward for their service. As a result, every soldier felt important in Napoleons Army. This is magnified with the near invincible nature of the French army until 1809, and even then the French army still was sure if itself.

To wrap up, the French had the stamina to fight for twenty years because they benefited from it,more than from any other time. There was far more social mobility and self worth in the Napoleonic era than during the Ancien Regime.

Edit: Sources

Napoleons Infantry Handbook by Terry Crowdy

*Swords Around A Throne" by John Elting

Napoleon: A Life by Andrew Roberts

The Campaigns of Napoleon by David G. Chandler