I calibrated the instrument and checked with different materials. For one particular type of material I am getting this behavior. I attached the nyquist plot. Please see if you could help me.
I worked with 2 HP impedance briges, which covered range from 5 Hz to 1 GHz. Near the lower range 5 Hz data reading was always unstable. But at w=1 KHz the reading was always stable and reproducable, and, for all systems I measured no changes were monitored up to 10 Khz. So, the value of that flat line I attributed to Low Frequency Conductivity/ or Impedance. Try to check my claim, this might work for you as well.
Probably the experimental system you are measuring is unstable and so at low frequencies the impedance of the system is changing. One way to test this out would be to immediately repeat your impedance spectrum, but scan from low frequency to high frequency. If your data now traces a smaller semi circle then this probably indicates that your system is not stable.