The effect of the hyperon softening of the equation of state (EOS) of dense matter on the spin evolution of isolated neutron stars is studied for a broad set of hyperonic EOSs. We use a multidomain 2-D code based on a spectral method, and show how important the precision of solving the equations of stationary motion is for the stability analysis. For some EOSs, the hyperon softening leads to spin-up by angular momentum loss, in the form of the back-bending phenomenon, for a rather broad range of stellar baryon mass. We show that large segments of the evolutionary tracks exhibiting the back-bending behaviour in the moment-of-inertia - rotation-frequency plane are unstable and therefore not astrophysically relevant. We show also that during the spin-up - angular-momentum-loss epoch, an isolated neutron star (e.g. a radio pulsar) can lose a sizable part of its initial angular momentum without significantly changing its rotation period. We propose also simple arguments and criteria allowing one to connect the presence of a back-bending epoch with the mass-radius relations and the stiffness and/or softness of the nucleon and hyperon EOSs of the neutron star core.