I think that Hawthorne's description of "human frailty" and "sorrow" applies more to the Reverend Arthur Dimmesdale than to Hester Prynne. He dies having never come to terms with his sin and having only found the courage to admit it publicly mere moments before his pathetic death. Even on the night of Governor Winthrop's death, when Pearl, Dimmesdale's little girl, asked him if he would stand with them on scaffold during the day, he refuses her. He is weak. He tortures himself for years rather than confess, telling everyone how awful he is, what a terrible sinner, influencing them to think that he's so much more saintly. If anyone is frail here, it is he.

Hester, on the other hand, is anything but frail. She endures, for seven long years. She could've moved away or gone home. Instead, she chooses to remain because she wants to be near the man she loves. She raises her wild daughter alone, and then must surely experience a great deal of joy watching her grow into a woman in Europe after Dimmesdale's death. Hester doesn't have to come back to Boston, but she does. She chooses to once again embrace her punishment, the scarlet letter, because it is the closest she can be to the man she loved. She doesn't die in shame, but rather as a symbol of helpfulness and selflessness, using her final years to help others. She reassures and comforts those women, who especially need it, saying, 

at some brighter period, when the world should have grown ripe for it, in Heaven's own time, a new truth would be revealed, in order to establish the whole relation between man and woman on a surer ground of mutual happiness. 

She may feel sorrow, and she may still feel shame for her sin, but Hester is strong and forward-thinking.