In this paper it is shown that a general SIR epidemic model, with the force of infection subject to seasonal variation, and a proportion of the number of infectives measured, is unidentifiable. This means that an uncountable number of different parameter vectors can, theoretically, give rise to the same idealised output data. Any subsequent parameter estimation from real data must be viewed with less confidence as a result. The approach is essentially that developed by Evans et al. (2002), with modifications to allow for time-variation in the effective contact rate. This approach utilises the existence of an infinitely differentiable transformation that connects the state trajectories corresponding to parameter vectors that give rise to identical output data.