The Type I Seyfert galaxy Markarian 509 was observed with Suzaku in 2010 November, for a gross time span of 2.2 days. The timing and spectral properties of the 0.5-45 keV X-rays, detected with the XIS and HXD, consistently revealed the presence of a soft spectral component that remained constant while the total X-ray intensity varied by +/- 10%. This stable soft component, found in the 0.5-3.0 keV range, was interpreted as being a result of thermal Comptonization in a corona with a temperature of similar to 0.5 keV and an optical depth of similar to 18. The time-avearged 0.5-45 keV Suzaku spectrum was reproduced successfully, as a combination of this thermal Comptonization component, a harder power-law of photon index similar to 1.8, moderate reflection, and an iron K-emission line. By analyzing four archival Suzaku datasets of the same object obtained in 2006, the thermal Comptonization component, which was stable during 2.2-day pointing in 2010, was found to vary on time scales of a few weeks, independently of the power-law component. Implications of these results are discussed in terms of a "multi-zone Comptonization" view, obtained with Suzaku from the black-hole binary Cygnus X-1.