check out our:
He himself, on the other hand, with characteristic humility, avowed his belief that if Providence should see fit to remove him, it would be because of his own unworthiness to perform its humblest mission here on earth. (9.3)
Dimmesdale sees everything—his life, work, and death—as being out of his power. Maybe that's why he keeps begging Hester to reveal his secret. He can't take a single action for himself; it's not what he believes.
These questions were solemnly propounded to Mr. Dimmesdale by the elder ministers of Boston and the deacons of his church, who, to use their own phrase, “dealt with him” on the sin of rejecting the aid which Providence so manifestly held out. He listened in silence, and finally promised to confer with the physician. (9.7)
Dimmesdale wants to let himself die, but he's not allowed to: it would be a sin to refuse Chillingworth's help. (This kind of logic gets tricky once you start adding life-support machines into the mix.)
“At the great judgment day,” whispered the minister—and, strangely enough, the sense that he was a professional teacher of truth impelled him to answer the child so. “Then, and there, before the judgment seat, thy mother, and thou, and I, must stand together. But the daylight of this world shall not see our meeting!” (12.28)
Check out the word "must": at some point, it's all going to be taken out of Dimmesdale's hand, and the whole mess will be revealed—to God. But at this point, he still seems to think that he doesn't have the will to reveal it himself.