Beware the recent past: a bias in spectral energy distribution modelling due to bursty star formation

We investigate how the recovery of galaxy star formation rates (SFRs) using energy-balance spectral energy distribution (SED) fitting codes depends on their recent star formation histories (SFHs). We use the Magphys and Prospector codes to fit 6,706 synthetic spectral energy distributions of simulated massive galaxies at $1 < z < 8$ from the Feedback in Realistic Environments (FIRE) project. We identify a previously-unknown systematic error in the Magphys results due to bursty star formation: the derived SFRs can differ from the truth by as much as 1 dex, at large statistical significance ($>5\sigma$), depending on the details of their recent SFH. SFRs inferred using Prospector with non-parametric SFHs do not exhibit this trend. We show that using parametric SFHs (pSFHs) causes SFR uncertainties to be underestimated by a factor of up to $5\times$. Although this undoubtedly contributes to the significance of the systematic, it cannot explain the largest biases in the SFRs of the starbursting galaxies, which could be caused by details of the stochastic prior sampling or the burst implementation in the Magphys libraries. We advise against using pSFHs and urge careful consideration of starbursts when SED modelling galaxies where the SFR may have changed significantly over the last ~100 Myr, such as recently quenched galaxies, or those experiencing a burst. This concern is especially relevant, e.g. when fitting JWST observations of very high-redshift galaxies.