The negative dielectric loss may occur, but rarely. Common examples concern ferro-matterials (near resonance frequency Fr). Left and right from Fr we have both modes e.g. strong positive & negative dielectric loss.
After a certain temperature the conductivity of the ceramic pallet becomes very high. In this case the test circuit behaves like inductive and system displays negative capacitance and loss factor.
Please check the ceramic pellets on both sides, of the electrodes and sample holder. I too face this type of problems and it is common in ceramics at high temperatures.
What do you measure is some effective parameters of the material which is in this case is the ceramic. The behavior of ceramic as a function of the applied field and temperature is known. Any appreciable deviation from this behavior may be due to the parasitic elements in the measurement specially the the metal ceramic electrodes. The ceramic conductivity can increase such that it becomes semiconducting and the metal ceramic interfaces may play a predominate role on the terminal impedance. So, you have to be sure to exclude the effect of the interfaces before interpreting the results. One method is to use the impedance spectroscopy to separate the effect of the electrodes from bulk material.