We investigate model based classification with partially labelled training data. In many biostatistical applications, labels are manually assigned by experts, who may leave some observations unlabelled due to class uncertainty. We analyse semi-supervised learning as a missing data problem and identify situations where the missing label pattern is non-ignorable for the purposes of maximum likelihood estimation. In particular, we find that a relationship between classification difficulty and the missing label pattern implies a non-ignorable missingness mechanism. We examine a number of real datasets and conclude the pattern of missing labels is related to the difficulty of classification. We propose a joint modelling strategy involving the observed data and the missing label mechanism to account for the systematic missing labels. Full likelihood inference including the missing label mechanism can improve the efficiency of parameter estimation, and increase classification accuracy.