The stability of the spin-precession currents in superfluid He-3-B is analyzed for the precession angle very close to 104 degrees. In this limit, a spin-precession vortex has a very large core, and the barrier that blocks motion of these large-core vortices across the current streamlines (phase slip) disappears at precession-phase gradients much smaller than critical gradients estimated from the Landau criterion. Nevertheless, spin-precession currents remain stable up to the Landau-critical gradients, since, in this case, there is a barrier, which blocks the phase slip at a very early stage of the vortex-core nucleation. The second-order phase transition between the parity-symmetric and parity-asymmetric spin-precession vortex cores at the precession angle of 126.5 degrees is also predicted.
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