Yes the holding of Iwo Jima inspires 1million man hours of work in the Japanese homeland and when it is captured they get discouraged and leave their jobs.
When you put it that
way, it sure does sound odd.
Nevertheless, sometimes that's the way that these human intangibles like 'morale' actually behave.
Think about it: as a Japanese citizen, why would you keep slaving for the Imperial cause (say, digging coal) if you knew that the war was a lost cause, and that the Empire would be dismantled by the Americans in a matter of weeks? And what better sign that the US is winning in the Pacific than by their taking an island within comfortable bombing distance of Tokyo, with no other land mass in the way to stop them from doing so?
Under those circumstances, if you were at all aware of the gravity of the situation (about to be firebombed and then nuked... twice!), you'd be running to find a nice cave to shelter in, rather than clocking in for work as usual.
Losing Iwo Jima: 1 IPC.
Saving your own a$$: priceless.