  The Born-Infeld determinantal gravity has been recently proposed as a way to
smooth the Big Bang singularity. This theory is formulated on the Weitzenbock
space-time and the teleparallel representation is used instead of the standard
Riemannian representation. We find that although this theory is shown to be
singularity-free for certain region of the parameter space in which the
divergence of the Hubble rate at the high energy regime is substituted by a
de-Sitter stage or a bounce in a Friedmann-Lemaitre-Robertson-Walker universe,
cosmological singularities such as Big Rip, Big Bang, Big Freeze, and Sudden
singularities can emerge in other regions of the configuration space of the
theory. We also show that all these singular events exist even though the
Universe is filled with a perfect fluid with a constant equation of state.
