  Context. J1407 (1SWASP J140747.93-394542.6 in full) is a young star in the
Scorpius-Centaurus OB association that underwent a series of complex eclipses
over 56 days in 2007. To explain these, it was hypothesised that a secondary
substellar companion, J1407b, has a giant ring system filling a large fraction
of the Hill sphere, causing the eclipses. Observations have not successfully
detected J1407b, but do rule out circular orbits for the companion around the
primary star.
  Aims. We test to what degree the ring model of J1407b could survive in an
eccentric orbit required to fit the observations.
  Methods. We run N-body simulations under the AMUSE framework to test the
stability of Hill radius-filling systems where the companion is on an eccentric
orbit.
  Results. We strongly rule out prograde ring systems and find that a secondary
of 60 to 100MJup with an 11 year orbital period and retrograde orbiting
material can survive for at least $10^4$ orbits and produce eclipses with
similar durations as the observed one.
