Spinning rigid bodies are stable about their axes of smallest and largest moments of inertia. When there are energy dissipation modes, such as bending and propellant slosh, only the largest moment of inertia axis is stable, because rotating about that axis corresponds to least kinetic energy. This is why the Explorer 1's spin stabilization failed (the radio antennae flexed to dissipate energy).
However, rockets that are spin-stabilized are also rotating about their axis of smallest moment of inertia (they are "minor axis spinners"). Since rockets bend and their propellant sloshes, shouldn't this rotation be unstable? My question is whether the reason why spin stabilization works for a rocket's attitude is because the flight time is much less than the time it would take for the rotational instability to grow? Or do rockets use active control systems to stabilize the minor spin axis?
Note that an answer to a previous question seems to indicate that spin-stabilization would be unstable for a rocket - however there's no explanation as to how this problem is dealt with.