There are different definitions of dielectric susceptibility. One is a "static" (I don't know if this is the correct term), defined as:
[tex]
P_{i} = \epsilon_{0} \, \sum_{k}{\chi_{i k} \, E_{k}}[/tex]
for linear media, i.e. media where the polarization is always proportional to the existing electric field; and the other is "dynamic" (agaim, terminology), defined as the tensor:
[tex]
\chi_{i k} = \frac{1}{\epsilon_{0}} \, \frac{\partial D_{i}}{\partial E_{k}}[/tex]
For isotropic materials, [itex]\chi_{i k} = \chi \, \delta_{i k}[/itex].
The dielectric permittivity tensor is defined through the susceptibility tensor as:
[tex]
\epsilon_{i k} = \epsilon_{0} \, \left(\delta_{i k} + \chi_{i k}\right)[/tex]
or for isotropic media ([itex]\epsilon_{i k} = \epsilon \, \delta_{i k}[/itex]):
[tex]
\epsilon = \epsilon_{0} \, (1 + \chi)[/tex]
so, in infinite permittivity would correspond to infinite susceptibility. I would suspect that this refers to the second definition, i.e. a susceptibility of the "dynamical" kind and corresponds to a vertical tangent on the P - E plot (or D - E plot).
If you know thermodynamics, you will see that the susceptibility corresponds to a second derivative of the Helmholtz free energy with respect to the field, and according to the Ehrenfest classification of phase transitions, this would indicate a second order phase transition (or a critical point).