The flat spectrum radio quasar (FSRQ) PKS 0208-512 underwent three outbursts at the optical-near-infrared (OIR) wavelengths during 2008-2011. The second OIR outburst did not have a gamma-ray counterpart despite being comparable in brightness and temporal extent to the other two. We model the time variable spectral energy distribution of PKS 0208-512 during those three flaring episodes with leptonic models to investigate the physical mechanism that can produce this anomalous flare. We show that the redder-when-brighter spectral trend in the OIR bands can be explained by the superposition of a fixed thermal component from the accretion disk and a synchrotron component of fixed shape and variable normalization. We estimate the accretion disk luminosity at L_d ~8 X 10^45 erg/s. Using the observed variability timescale in the OIR band t_{var,obs} ~2 d and the X-ray luminosity L_X ~3.5 X 10^45 erg/s, we constrain the location of the emitting region to distance scales that are broadly comparable with the dusty torus. We show that variations in the Compton dominance parameter by a factor of ~4 --- which may result in the anomalous outburst --- can be relatively easily accounted for by moderate variations in the magnetic field strength or the location of the emission region. Since such variations appear to be rare among FSRQs, we propose that most gamma-ray/OIR flares in these objects are produced in jet regions where the magnetic field and external photon fields vary similarly with distance along the jet, e.g., u_B ~u_ext ~r^{-2}.
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