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Résumé : We study the dynamics and stability in a strongly-interacting resonantly-driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the dynamics is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is quick in these two regimes (but to different "temperatures"), in the crossover between them we find slow glassy dynamics: temporal fluctuations become strong and temporal correlations long-lived. Microscopically, we trace back the origin of this glassy dynamics to the appearance of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the metastable energy conservation, and thus produces thermalization to infinite temperature.