It has recently been suggested that the eclipsing polar HU Aquarii is a host to at least two giant planets. We have performed highly detailed dynamical analyses of the orbits of those planets and showed that the proposed system is highly unstable on time-scales of <5 × 103 yr. For the coplanar orbits suggested in the discovery Letter, we find stable orbital solutions for the planetary system only if the outer body moves on an orbit that brings it no closer to the host star than ∼6 au. The required periastron distance for the outer planet lies approximately 5 Hill radii beyond the orbit of the inner planet, and well beyond the 1σ error bars placed on the orbit of the outer planet in the discovery Letter. If the orbits of the proposed planets are significantly inclined with respect to one another, the median stability increases slightly, but such systems still become destabilized on astronomically minute time-scales (typically within a few 104 yr). Only in the highly improbable scenario where the outer planet follows a retrograde but coplanar orbit (i.e. inclined by 180° to the orbit of the inner planet) is there any significant region of stability within the original 1σ orbital uncertainties. Our results suggest that, if there is a second (and potentially, a third planet) in the HU Aquarii system, its orbit is dramatically different from that suggested in the discovery Letter, and that more observations are critically required in order to constrain the nature of the suggested orbital bodies.