  In this work we analyze the tensor-force component of effective interactions
appropriate for nuclear shell-model studies, with particular emphasis on the
monopole term of the interactions. Standard nucleon-nucleon ($NN$) interactions
such as AV8' and $\chi$N$^3$LO are tailored to shell-model studies by employing
$V_{low k}$ techniques to handle the short-range repulsion of the $NN$
interactions and by applying many-body perturbation theory to incorporate
in-medium effects. We show, via numerical studies of effective interactions for
the $sd$ and $pf$ shells, that the tensor-force contribution to the monopole
term of the effective interaction is barely changed by these renormalization
procedures, resulting in almost the same monopole term as the one of the bare
$NN$ interactions. We propose to call this feature {\it Renormalization
Persistency} of the tensor force, as it is a remarkable property of the
renormalization and should have many interesting consequences in nuclear
systems. For higher multipole terms, this feature is maintained to a somewhat
smaller extent. We present general intuitive explanations for the
renormalization persistency of the tensor force, as well as analyses of
core-polarization terms in perturbation theory. The central force does not
exhibit a similar renormalization persistency.
