  For a class of frustrated antiferromagnetic spin lattices (in particular, the
square-kagom\'{e} and kagom\'{e} lattices) we discuss the impact of recently
discovered exact eigenstates on the stability of the lattice against
distortions. These eigenstates consist of independent localized magnons
embedded in a ferromagnetic environment and become ground states in high
magnetic fields. For appropriate lattice distortions fitting to the structure
of the localized magnons the lowering of magnetic energy can be calculated
exactly and is proportional to the displacement of atoms leading to a
spin-Peierls lattice instability. Since these localized states are present only
for high magnetic fields, this instability might be driven by magnetic field.
The hysteresis of the spin-Peierls transition is also discussed.
