Low loss, polarisation-maintaining, all-fibre ring resonators can exhibit non-linear propagation effects occurring at relatively low input powers. Observations have been made of Stimulated Brillouin Scattering (SBS) with input powers of 65μW leading to significant non-linear variations in the measured value of finesse, due to depletion of the power via the SBS process. Variations of measured finesse from 210 to 320 have been observed for a variation in input power of 155 p.W. The nature of this variation in resonator finesse with input power has been studied and is shown to depend upon the level of the input power when the resonator response is optimised.