I agree that there are many components to Hester's refusal to reveal Arthur as the father of her child. One which has not been mentioned but I think has merit is that she is hopeful they can resume their relationship one day. It's clear that Hester never stops loving Arthur (though he does not appear to share those sentiments in the face of his guilty conscience) and, like most women would be, she is hopeful she can be with him again at some point in time. If she tells, there is no chance of that ever happening.
Interestingly enough, I've always thought there was a point in their journey when the town just might have accepted Hester and Arthur as a couple with Pearl as their child. At the beginning, though, there is just too much for Hester to lose by telling.
Actually, there's one interesting part of The Scarlet Letter where Hester talks about the reason herself:
"Speak out the name! That, and thy repentance, may avail to take the scarlet letter off thy breast."
"Never! ... It is too deeply branded. Ye cannot take it off. And would that I might endure his agony as well as mine! ... I will not speak! ... And my child must seek a heavenly father, she shall never know an earthly one!"
I think this passionate statement by Hester speaks volumes. (My, Hester's passionate about everything she does, isn't she?) To me, it says that Hester's reasoning is nothing short of admirable. It recognizes that what she feels is absolute "agony," and that her greatest desire is to prevent that same agony for Dimmesdale. This also hints that she might also still feel a great deal of love for him, ... the father of her child. Yep, Hester's already on her way to that "A" standing for "Able" instead of "Adultery."
I believe Hester refuses to reveal her partner's sin for many reasons.
First, I think she knew she was stronger than Dimmesdale. She had the fortitude to withstand the criticism that would come after a transgression like adultery, whereas she knew her love was a sensitive soul and she was afraid of what the backlash might do to him.
Also, she wanted to protect him because she loved him very much. Hester did not want her beloved Arthur to suffer so she kept his secret.
But, I believe, that she also did it partially out of spite. I think she was so sick of the judgment and hypoccrisy of the purtian people, that she puposely hid her partner's name from them to make them angry because she did not respect the people around her.
Finally, I think she believed it was none of their business. That what happened between she and Dimmesdale was private, and nothing they should be concerned about.