  We explore prethermal Floquet steady states and instabilities of the weakly
interacting two-dimensional Bose-Hubbard model subject to periodic driving. We
develop a description of the nonequilibrium dynamics, at arbitrary drive
strength and frequency, using a weak-coupling conserving approximation. We
establish the regimes in which conventional (zero-momentum) and unconventional
[$(\pi,\pi)$-momentum] condensates are stable on intermediate time scales. We
find that condensate stability is \emph{enhanced} by increasing the drive
strength, because this decreases the bandwidth of quasiparticle excitations and
thus impedes resonant absorption and heating. Our results are directly relevant
to a number of current experiments with ultracold bosons.
