  The Eddington-inspired-Born-Infeld (EiBI) theory has been recently
resurrected. Such a theory is characterized by being equivalent to Einstein
theory in vacuum but differing from it in the presence of matter. One of the
virtues of the theory is to avoid the Big Bang singularity for a radiation
filled universe. In this paper, we analyze singularity avoidance in this kind
of model. More precisely, we analyze the behavior of a homogeneous and
isotropic universe filled with phantom energy in addition to the dark and
baryonic matter. Unlike the Big Bang singularity that can be avoided in this
kind of model through a bounce or a loitering effect on the physical metric, we
find that the Big Rip singularity is unavoidable in the EiBI phantom model even
though it can be postponed towards a slightly further future cosmic time as
compared with the same singularity in other models based on the standard
general relativity and with the same matter content described above.
