  We investigate whether the emission of neutrinos observed in 2014-15 from the
direction of the blazar TXS 0506+056 can be accommodated with leptohadronic
multi-wavelength models of the source commonly adopted for the 2017 flare.
While multi-wavelength data during the neutrino flare are sparse, the large
number of neutrino events ($13\pm5$) challenges the missing activity in gamma
rays. We illustrate that two to five neutrino events during the flare can be
explained with leptohadronic models of different categories: a one-zone model,
a compact core model, and an external radiation field model. If, however,
significantly more events were to be accommodated, the predicted
multi-wavelength emission levels would be in conflict with observational X-ray
constraints, or with the high-energy gamma ray fluxes observed by the Fermi
LAT, depending on the model. For example, while the external radiation field
model can predict up to five neutrino events without violating X-ray
constraints, the absorption of high-energy gamma rays is in minor tension with
data. We therefore do not find any model that can simultaneously explain the
high event number quoted by IceCube and the (sparse) electromagnetic data
during the neutrino flare.
