The polarization characteristics of ohmic and (Al-)Schottky type CdTe sensors supplied by Acrorad have been characterized with the low noise, charge integrating readout chip JUNGFRAU, revealing defined areas in the Schottky type sensors, which were irradiated with 20 keV photons in previous experiments more than one year ago. These areas, which have absorbed doses of up to 1079 kGy, show a more robust charge collection compared to unirradiated areas. In contrast to this, no alteration of the polarization characteristics could be found in ohmic type CdTe sensors after irradiation. The polarization behavior of the sensors has been characterized in-situ over time and at different temperatures by using an homogeneous, low flux molybdenum fluorescence illumination. An increase of the leakage current in the irradiated areas was found and quantified as a function of absorbed dose as well as its influence on the stability on the number of photon counts. In addition to the influence of X-ray irradiation, the effect of thermal annealing on the polarization characteristics of Schottky type CdTe sensors has been studied. Possible routes for the usage of Schottky type CdTe sensors in synchrotron applications are outlined in this publication.