  Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave
interferometers. We investigate the dynamics and stability of bright-soliton
wave packets in one-dimensional tilted optical lattices with a modulated
mean-field interaction $g(t)$. By means of a time-reversal argument, we prove
the stability of Bloch oscillations of breathing solitons that would be
quasistatically unstable. Floquet theory shows that these breathing solitons
can be more stable against certain experimental perturbations than rigid
solitons or even non-interacting wave packets.
