ISTM it relates to " If a woman conceals her affection with the same skill from the object of it, she may lose the opportunity of fixing him." The romantic theory that if a man loves a woman then nothing will deter him from persisting in that love, and that a show of indifference may indeed stimulate him to even greater heights of love is doubted by Charlotte. She thinks that a natural preference may exist and predispose a man towards a woman but that this may wither away if all the other feelings which simultaneously exist in any person, the need to feel liked, approved of and valued for example, are ignored or slighted.
ISTM that the rewritten third sentence conveys a different meaning. Ms Austen surely intended us to understand that the new relationship is based on friendship and esteem whereas the AI suggests that the previous relationship was the subject of the sentence’s second. clause.