  We consider Bloch oscillations of Bose-Einstein condensates in presence of a
time-modulated s-wave scattering length. Generically, interaction leads to
dephasing and decay of the wave packet. Based on a cyclic-time argument, we
find---additionally to the linear Bloch oscillation and a rigid soliton
solution---an infinite family of modulations that lead to a periodic time
evolution of the wave packet. In order to quantitatively describe the dynamics
of Bloch oscillations in presence of time-modulated interactions, we employ two
complementary methods: collective-coordinates and the linear stability analysis
of an extended wave packet. We provide instructive examples and address the
question of robustness against external perturbations.
