The impact of Brillouin scattering on the polarisation of pump and probe in a Brillouin optical-time domain analyser is investigated. Experimental results indicate that the Brillouin interaction integrated along the entire sensing fibre produces a polarisation pulling force that changes the pump polarisation. Although this force can be compensated to first order by dual-sideband probes, the Brillouin gain/loss experienced by probe bands induce a net pulling that leads to uncompensated polarisation fading and reduced signal-to-noise ratio. While the use of two simultaneous orthogonally-polarised probes alleviates fading issues, spectral distortions originate from the coupling between Brillouin gain and polarisation pulling.