The planar arrangement of nearly half the satellite galaxies of M31 has been a source of mystery and speculation since it was discovered. With a growing number of other host galaxies showing these satellite galaxy planes, their stability and longevity have become central to the debate on whether the presence of satellite planes are a natural consequence of prevailing cosmological models, or represent a challenge. Given the dependence of their stability on host halo shape, we look into how a galaxy plane's dark matter environment influences its longevity. An increased number of dark matter subhaloes results in increased interactions that hasten the deterioration of an already-formed plane of satellite galaxies in spherical dark haloes. The role of total dark matter mass fraction held in subhaloes in dispersing a plane of galaxies presents non-trivial effects on plane longevity as well. But any misalignment of plane inclines to major axes of flattened dark matter haloes lead to their lifetimes being reduced to ≤3 Gyr. Distributing ≥40 per cent of total dark mass in subhaloes in the overall dark matter distribution results in a plane of satellite galaxies which is prone to change through the 5-Gyr integration time period.