The edge-on debris disc of the nearby young star Beta Pictoris shows an unusual brightness asymmetry in the form of a clump. The clump has been detected in both the mid-infrared (IR) and CO, and its origin has so far remained uncertain. Here, we present new mid-IR observations of Beta Pic to track any motion of the dust clump. Together with previous observations, the data span a period of 12 yr. We measured any projected displacement of the dust clump over the 12-yr period to be au away from the star based on the median and 1 sigma uncertainty, and constrain this displacement to be <11 au at the 3 sigma level. This implies that the observed motion is incompatible with Keplerian motion at the 2.8 sigma level. It has been posited that a planet migrating outwards may trap planetesimals into a 2:1 resonance, resulting in the observed clump at pericentre of their orbits that trails the planet. The observed motion is also incompatible with such resonant motion at the 2.6 sigma level. While Keplerian motion and resonant motion is still possible, the data suggest that the dust clump is more likely stationary. Such a stationary dust clump could originate from the collision or tidal disruption of a planet-sized body, or from secular perturbations due to a planet that create regions with enhanced densities in the disc.