We present a new five-epoch Chandra X-ray Observatory monitoring survey of the nearby spiral galaxy M33 which probes X-ray variability with time sampling between two weeks and four months. We characterize the X-ray variability of 55 bright point sources outside of the nucleus, many of which are expected to be high-mass X-ray binaries (HMXBs). We detect eight new candidate transients not detected in previous X-ray catalogs of M33 and discuss their possible nature. The final catalog includes 26 known HMXB candidates identified in the literature. We extend the baseline of the X-ray light curves up to 21 yr by including archival X-ray observations of these sources. We compare the detection and nondetection epochs of the sources to suites of simulated source duty cycles and infer that most of our detected sources have duty cycles >30%. We find only four sources whose detection patterns are consistent with having duty cycles below 30%. This large fraction of sources with high duty cycles is unexpected for a population of HMXBs; thus more frequent X-ray monitoring will likely reveal many more low duty cycle HMXBs in M33.