Why should this be? Of course, it is a ramification of patriarchy, but more specifically it has to do with women serving as guarantors of property transfers and then serving as illiquid stores of value after the key transaction they have facilitated has been executed. Women must be constant in their "love" so that property is passed along in an orderly fashion within approved family lines through marriages; this keeps "value" from becoming too mobile and disseminating itself more generally and yielding a more egalitarian society (or at least a society with enough mobility to make its losers restive and willing to rebel against the established order).
Trollope takes this for granted, which allows him to toss off lines like the following, summing up the whole of the patriarchal social structure in the height of its resistance to capitalism's creative destruction. In this passage, Johnny Eames is embarrassed by his benefactor's willingness to give him capital, which is a necessary prerequisite to his proposing to the jilted Lily Dale, niece of the squire.
He did not know whether it would be right in him to accept such pecuniary liberality from any living man, and almost thought that he should feel himself bound to reject the earl's offer. As to the squire's money, that he knew he might accept. All that comes in the shape of a young woman's fortune may be taken by any man.That's a pretty naked, almost astonishing, statement of the rules governing social relations in the upper-middle classes in Victorian England. Men can't give property to one another -- that suggests a dangerous liberality that can upset the established hierarchy. Marriage functions as a vetting process that permits such transfers out of the family -- or consolidates property according to the wishes of scions. (Not by accident does much of the novel's plot revolve around Lily's sister Bell refusing to marry her cousin Bernard Dale, an arrangement the squire demands. Not by accident does Clarissa have the same basic plot about compelled marriage for the sake of property management.) The point is that woman's constancy certifies (perhaps only metaphorically, in the symbolic economy of novels) her fitness as a financial instrument that makes property liquid for a brief window of time within the constraints of social custom.
Lily Dale's stubborn faithfulness to Crosbie, who dumped her for an aristocrat when he discovered she had no money to bring to a marriage, seems almost to make a deliberate mockery of the expectations placed on women. Having been valued once, she refuses to be repriced in a secondary market. She represents a kind of opportunity cost or a frozen asset; she refuses to facilitate the property shift the earl wants to engender for Eames's benefit, and he is forced to work outside the established system, helping usher in its eventual destruction. Soon it will be impossible to use marriage to preserve the aristocratic order; soon there will just be capital circulating freely.
Here's how she describes her stubbornness: "What can a heart be worth if it can be transferred hither and thither as circumstance and convenience and comfort may require?" She seems to believe that limiting herself to being used for only one exchange (that failed) preserves her value (in the form of self-worth). Another way to put that is that she has value to herself only when she can't be exchanged or facilitate exchange; her self-value disappears when she becomes the mere conduit for value transfers between other parties. So she takes an unfair system to its absurd extreme to illustrate just how intransigent women must be to retain self-worth when they are begrudgingly permitted only one significant decision in their lives (who to marry). This is why some commentators interpret Lily Dale as being in love with herself and glad to be jilted -- she gets to have the value of her choice continually reinforced with none of the unpleasantness of outgrowing that choice once consummated and watching its significance dwindle.
But the underlying tragedy her situation suggests is that women can't feel themselves to be appreciated within the context of ordinary domesticity -- the happy life that Crosbie is often depicted as imagining in despair from within the domestic hell of life with Lady Alexandrina. Instead female self-worth depends on being suspended in pre-matrimonial limbo, affianced but never married. They can only have a kind of fictitious, theoretical value that finds no expression in the everyday practice of adult love.