  We study the Bloch oscillations (BOs) of two-component Bose-Einstein
condensates (BECs) trapped in spin-dependent optical lattices. Based on the
derived equations of motion of the wave packet in the basis of localized wave
functions of the lattice sites, the damping effect induced by the
intercomponent and intracomponent interactions to the BOs is explored
analytically and numerically. We also show that such damping of the BOs can be
suppressed entirely if all the atom-atom interactions are modulated
synchronously and harmonically in time with suitable frequency via the Feshbach
resonance. When the intercomponent and the intracomponent interactions have
inverse signs, we find that the long-living BOs and even the revival of the BOs
can be achieved via only statically modulating the configuration of optical
lattices. The results provide a valuable guidance for achieving long-living BOs
in the two-component BEC system by the Feshbach resonances and manipulating the
configuration of the optical lattices.
