Question: Poor performance of Statistics[NonlinearFit]

I'm trying to approximate points with a function of certain form with Statistics[NonlinearFit]. I expect the graph in the second example to be closely approximate of the points, just like the first graph. For some reason, the second graph is way off. Seems like a bug. Any suggestions are highly appreciated.

Here is the code

plotApprox := proc(listName)
    local X, Y, convModel, modList;
    X:=map(p -> p[1],listName);
    Y:=map(p -> p[2],listName);
    convModel := Statistics[NonlinearFit]((A*n+B)/(n+C), X, Y, n);
    modList := map(p->[p[1], subs(n = p[1],convModel)], listName);
    print(plot({listName, modList}));
    print(convModel)
end:

trimList1 := [[0, .8353219697], [1, .7946969697], [2, .7572443182], [3, .6901041667],
[4, .6449337121], [5, .6060132576], [6, .5842803030], [7, .5483428030],
[8, .5374053030], [10, .4594223485], [12, .4266098485], [14, .3987215909],
[16, .3316761364], [20, .2958333333], [24, .2942234848], [28, .2662405303],
[32, .2523200758], [40, .2071496212], [48, .1886837121], [56, .1715435606],
[64, .1403409091], [80, .1215909091], [96, .1106534091], [112, .1012784091],
[128, 0.9507575758e-1], [160, 0.8096590909e-1], [192, 0.7476325758e-1],
[224, 0.6534090909e-1], [256, 0.5610795455e-1], [320, 0.4995265152e-1],
[384, 0.4218750000e-1], [448, 0.3593750000e-1], [512, 0.3276515152e-1]]:

plotApprox(trimList1);

trimList2 := [[0, 1.000000000], [1, .7729166667], [2, .6260416667], [3, .5843750000],
[4, .5270833333], [5, .4822916667], [6, .4572916667], [7, .4447916667],
[8, .4437500000], [10, .4052083333], [12, .3729166667], [14, .3552083333],
[16, .3479166667], [20, .3302083333], [24, .3083333333], [28, .3104166667],
[32, .2843750000], [40, .2427083333], [48, .2239583333], [56, .1895833333],
[64, .1333333333], [80, .1177083333], [96, .1010416667], [112, 0.9687500000e-1],
[128, 0.7708333333e-1], [160, 0.7708333333e-1], [192, 0.6458333333e-1], [224, 0.4166666667e-1]]:

plotApprox(trimList2);