  We report on the Swift-BAT detection of a short burst from the direction of
the TeV binary LS I +61 303, resembling those generally labelled as
magnetar-like. We show that it is likely that the short burst was indeed
originating from LS I +61 303 (although we cannot totally exclude the
improbable presence of a far-away line-of-sight magnetar) and that it is a
different phenomena with respect to the previously-observed ks-long flares from
this system. Accepting as a hypothesis that LS I +61 303 is the first magnetar
detected in a binary system, we study which are the implications. We find that
a magnetar-composed LS I +61 303-system would most likely be (i.e., for usual
magnetar parameters and mass-loss rate) subject to a flip-flop behavior, from a
rotational powered regime (in apastron) to a propeller regime (in periastron)
along each of the LS I +61 303, eccentric orbital motion. We prove that whereas
near apastron an inter-wind shock can lead to the normally observed LS I +61
303behavior, with TeV emission, the periastron propeller is expected to
efficiently accelerate particles only to sub-TeV energies. This flip-flop
scenario would explain the system's behavior where a recurrent TeV emission was
seen appearing near apastron only, the anti-correlation of GeV and TeV
emission, and the long-term TeV variability (which seems correlated to LS I +61
303's super-orbital period), including the appearance of a low TeV-state.
Finally, we qualitatively put the multi-wavelength phenomenology in context of
our proposed model, and make some predictions for further testing.
