When the Russian army mounted a full-scale invasion two years ago, Ukrainian men zealously rushed to recruitment centers across the country to enlist, ready to die in defense of their nation. Today, with Russia in control of roughly one-quarter of Ukraine and the two armies virtually deadlocked along a 1,000-kilometer (620-mile) front line, that spirit to enlist has faded: Many Ukrainian men are evading the draft by hiding at home or trying to bribe their way out of the battle. Along the frigid and muddy front line, commanders say their army is too small and made up of too many...