  We investigate a regular black hole model with a de Sitter-like core at its
center. This type of a black hole model with a false vacuum core was introduced
with the hope of singularity-resolution and is a common feature shared by many
regular black holes. In this paper, we examine this claim of a singularity-free
black hole by employing the thin-shell formalism, and exploring its dynamics,
within the Vaidya approximation. We find that during gravitational collapse,
the shell necessarily moves along a space-like direction. More interestingly,
during the evaporation phase, the shell and the outer apparent horizon approach
each other but, unless the evaporation takes place very rapidly, the
approaching tendency is too slow to avoid singularity-formation. This shows
that albeit a false vacuum core may remove the singularity along the ingoing
null direction, there still exists a singularity along the outgoing null
direction, unless the evaporation is very strong.
