Context. Understanding how accretion proceeds is a key question of star formation, with important implications for both the physical and chemical evolution of young stellar objects. In particular, very little is known about the accretion variability in the earliest stages of star formation. Aims. Our aim is to characterise protostellar accretion histories towards individual sources by utilising sublimation and freeze-out chemistry of CO. Methods. A sample of 24 embedded protostars are observed with the Submillimeter Array (SMA) in context of the large program "Mass Assembly of Stellar Systems and their Evolution with the SMA" (MASSES). The size of the C¹⁸O-emitting region, where CO has sublimated into the gas-phase, is measured towards each source and compared to the expected size of the region given the current luminosity. The SMA observations also include 1.3 mm continuum data, which are used to investigate whether or not a link can be established between accretion bursts and massive circumstellar disks. Results. Depending on the adopted sublimation temperature of the CO ice, between 20% and 50% of the sources in the sample show extended C¹⁸O emission indicating that the gas was warm enough in the past that CO sublimated and is currently in the process of refreezing; something which we attribute to a recent accretion burst. Given the fraction of sources with extended C¹⁸O emission, we estimate an average interval between bursts of 20 000-50 000 yr, which is consistent with previous estimates. No clear link can be established between the presence of circumstellar disks and accretion bursts, however the three closest known binaries in the sample (projected separations <20 AU) all show evidence of a past accretion burst, indicating that close binary interactions may also play a role in inducing accretion variability.