Gamma-ray flares from blazars have been suggested as ideal periods for the detection of high-energy neutrinos. Indeed, the first ∼3σ high-energy neutrino source association was based on the detection of a single neutrino (IC-170922) coincident with the flaring blazar TXS 0506+056. A follow-up analysis of IceCube archival data revealed a past "neutrino flare" (13 +/- 5 events within ~ 6 months) from the direction of TXS 0506+056 which, however, was not accompanied by any electromagnetic flare. Here, we investigate whether leptohadronic models of blazar emission can explain the 2014-15 neutrino flare without violating existing electromagnetic observations. To do so, we perform a wide scan of the available parameter space and numerically compute the neutrino and electromagnetic emission of the hadronic cascade for ~ 50 parameter sets. We explore both synchrotron-supported and Compton-supported electromagnetic cascades in the linear and non-linear regimes. We compare our model predictions against publicly available data from IceCube and Fermi-LAT and the X-ray upper limits we derived by analyzing archival BAT and MAXI data. We find no model that can simultaneously explain the neutrino flare and satisfy all electromagnetic constraints, thus implying the presence of more than one emitting regions in TXS 0506+056.