Why does the permittivity decreases when a voltage is applied on the sample. On applying voltage, the dipolar polarization will increase and therefore the permittivity should increase. Instead, why does it decrease?
When the polarization increases linearly with electric field this is not increasing permittivity, it is constant permittivity, which is what many materials have. For very high fields, as Behnam Farid says, the polarization saturates, or stops increasing, so the permittivity drops. The same happens with the permeability of magnetic materials, giving the S shaped curve that you may be more familiar with.