  Soft extended emission (EE) following initial hard spikes up to 100 seconds
was observed with {\em Swift}/BAT for about half of short-type gamma-ray bursts
(SGRBs). This challenges the conversional central engine models of SGRBs, i.e.,
compact star merger models. In the framework of the black hole-neutron star
merger models, we study the roles of the radial angular momentum transfer in
the disk and the magnetic barrier around the black hole for the activity of
SGRB central engines. We show that the radial angular momentum transfer may
significantly prolong the lifetime of the accretion process and multiple
episodes may be switched by the magnetic barrier. Our numerical calculations
based on the models of the neutrino-dominated accretion flows suggest that the
disk mass is critical for producing the observed EE. In case of the mass being
$\sim 0.8M_{\odot}$, our model can reproduce the observed timescale and
luminosity of both the main and EE episodes in a reasonable parameter set. The
predicted luminosity of the EE component is lower than the observed EE with
about one order of magnitude and the timescale is shorter than 20 seconds if
the disk mass being $\sim 0.2M_{\odot}$. {\em Swift}/BAT-like instruments may
be not sensitive enough to detect the EE component in this case. We argue that
the EE component would be a probe for merger process and disk formation for
compact star mergers.
