  We consider a class of doubly intermittent maps with critical points,
unbounded derivative and regularly varying tails. Under some mild assumptions
we prove the existence of a unique mixing absolutely continuous invariant
measure and give conditions under which the measure is finite. This extends
former work by Coates, Luzzatto and Mubarak to maps with regularly varying
tails. Particularly, we look at the boundary case where the behaviour of the
slowly varying function decides if the invariant measure is finite or infinite.
