  We investigate non-BPS exact solutions in ${\mathbb C}P^{N-1}$ sigma models
on ${\mathbb R}^1 \times S^{1}$ with twisted boundary conditions, by using the
Din-Zakrzewski projection method. We focus on the relation of the non-BPS
solutions to the ansatz of multi-instanton (bion) configurations and discuss
their significance in the context of the resurgence theory. We find that the
transition between seemingly distinct configurations of multi-instantons occur
as moduli changes in the non-BPS solutions, and the simplest non-BPS exact
solution corresponds to multi-bion configurations with fully-compressed double
fractional instantons in the middle. It indicates that the non-BPS solutions
make small but nonzero contribution to the resurgent trans-series as special
cases of the multi-bion configurations. We observe a generic pattern of
transitions between distinct multi-bion configurations (flipping partners),
leading to the three essential properties of the non-BPS exact solution: (i)
opposite sign for terms corresponding to the left and right infinities, (ii)
symmetric location of fractional instantons, and (iii) the transition between
distinct bion configurations. By studying the balance of forces, we show that
the relative phases between the instanton constituents play decisive roles in
stability and instability of the muli-instanton configurations. We discuss
local and global instabilities of the solutions such as negative modes and the
flow to the other saddle points, by considering the deformations of the non-BPS
exact solutions within our multi-instanton ansatz. We also briefly discuss some
classes of the non-BPS exact solutions in Grassmann sigma models.
