Honestly, as I see it, Atty. General Madigan has very little to gain from appealing the decision. As has been noted, she would be very unlikely to win an appeal to SCOTUS (either because SCOTUS refuses to hear the appeal at all or because they would likely rule against her) and another loss would be something of a black mark on her resume. More importantly, however, she would probably lose a lot of support from downstate where the idea of CC is popular. Remember that unlike her father, Speaker Michael Madigan, and Chicago Mayor Emmanuel who are insulated within their own districts, Lisa Madigan holds a statewide office and needs to retain at least some support from downstate in order to advance her political career as she obviously has ambition to.
It is important to remember that last year the IL legislature passed a CC bill (they just fell a few votes short of the 2/3 majority needed to override Gov. Quinn's veto) so its probably a fairly safe assumption that the majority of downstate voters, if not the majority of all IL voters, want CC. Contradicting the will of the voters is rarely a smart political move and while many in Chicago want her to appeal, I doubt she'd actually lose all that much support by failing to do so.
She could also make a fairly convincing argument that given the deep financial problems that the State of Illinois has right now that spending even more of the taxpayers' money on an unwinnable appeal makes little sense. The die is pretty much cast at this point: IL will have CC sooner or later. The only question that remains at this point is how much time, money, and headache will Springfield expend before they get there and I just don't see Atty. General Madigan having much to gain from drawing things out any more.
Come election time, I rather doubt that this is an issue Madigan's going to want to be talking about and the sooner she can get it over with, the sooner it can begin fading from voters' memories. The politically savvy move, I think, would be to not appeal and let the fight shift into the legislature. This would serve two purposes as I see it: it would get Lisa Madigan out of the issue and shift the voters' attention to the legislature rather than her.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar