I think Emma realizes she has neglected Jane by the standards of social etiquette—the fact Emma can realize a fault says something good about her character. Mr. Knightley’s errors do not prove he is wrong to wish Emma would live up to her duty. He is also not alone in believing Emma has neglected Jane in the past. Mrs. Weston who hates to see a wrong in Emma also believes she has not done what she ought by Jane:

"You are right Mrs. Weston," said Mr. Knightley warmly, "Miss Fairfax is as capable as any of us of forming a just opinion of Mrs. Elton. Could she have chosen with whom to associate, she would not have chosen her. But (with a reproachful smile at Emma) she receives attentions from Mrs. Elton, which nobody else pays her."

Emma felt that Mrs. Weston was giving her a momentary glance; and she was herself struck by his warmth. With a faint blush… (33)

Perhaps Jane is less reserved with Mrs. Elton due to the subjects of their conversation. Jane annoys Emma in being suspiciously reserved on the topics of Weymouth, Mr. Dixon and his marriage and Jane’s opinion of Frank. I think the evidence is Jane does not always stonewall in conversation. She does seem suspiciously reserved on other topics—even with Emma. When Emma says Jane will not be allowed to be indifferent to Mr. Elton’s matrimonial plans she (Darcy-like) admits to finding it difficult to be interested in strangers:

"When I have seen Mr. Elton," replied Jane, "I dare say I shall be interested -- but I believe it requires that with me. And as it is some months since Miss Campbell married, the impression may be a little worn off." (21)

In Darcy this has always seems to me a rather unreserved moment for him and I don’t see why it should not be so for Jane as well. Jane like other JA ladies is open in her expectations about the ball:

…she enjoyed the thought of it to an extraordinary degree. It made her animated -- open hearted -- she voluntarily said; -- "Oh! Miss Woodhouse, I hope nothing may happen to prevent the ball. What a disappointment it would be! I do look forward to it, I own, with very great pleasure." (30)

Jane was quite unreserved and obliging with Mr. John Knightley about herself, letters and her feelings:

"Ah! you are not serious now. I know Mr. John Knightley too well -- I am very sure he understands the value of friendship as well as any body. I can easily believe that letters are very little to you, much less than to me, but it is not your being ten years older than myself which makes the difference, it is not age, but situation. You have every body dearest to you always at hand, I, probably, never shall again; and therefore till I have outlived all my affections, a post-office, I think, must always have power to draw me out, in worse weather than to-day." (34)

If Emma had graciously pursued other topics rather than preserving in her questions about the Dixons and Frank it is probable Jane’s suspicious reserve would not have reared it annoying head. Why could Emma not respect Jane’s boundaries (even if she does not agree with them) and converse on other topics? Perhaps Emma’s persistence in following an unwelcome (and I feel at least partly impertinent) line of questioning gave Jane no opportunity or inclination to further their acquaintance at that moment.