We present a comparison of two Suzaku X-ray observations of the nearby (z = 0.184), luminous (L ∼ 10 erg s) type I quasar, PDS 456. A new 125 ks Suzaku observation in 2011 caught the quasar during a period of low X-ray flux and with a hard X-ray spectrum, in contrast with a previous 190 ks Suzaku observation in 2007 when the quasar appeared brighter and had a steep (Γ > 2) X-ray spectrum. The 2011 X-ray spectrum contains a pronounced trough near 9 keV in the quasar rest frame, which can be modeled with blueshifted iron K-shell absorption, most likely from the He- and H-like transitions of iron. The absorption trough is observed at a similar rest-frame energy as in the earlier 2007 observation, which appears to confirm the existence of a persistent high-velocity wind in PDS 456, at an outflow velocity of 0.25-0.30c. The spectral variability between 2007 and 2011 can be accounted for by variations in a partial covering absorber, increasing in covering fraction from the brighter 2007 observation to the hard and faint 2011 observation. Overall, the low-flux 2011 observation can be explained if PDS 456 is observed at relatively low inclination angles through a Compton-thick wind, originating from the accretion disk, which significantly attenuates the X-ray flux from the quasar.