Recently it has been proposed that information in working memory (WM) may not always be stored in persistent neuronal activity but can be maintained in 'activity-silent' hidden states, such as synaptic efficacies endowed with short-term synaptic plasticity. To test this idea computationally, we investigated recurrent neural network models trained to perform several WM-dependent tasks, in which WM representation emerges from learning and is not a priori assumed to depend on self-sustained persistent activity. We found that short-term synaptic plasticity can support the short-term maintenance of information, provided that the memory delay period is sufficiently short. However, in tasks that require actively manipulating information, persistent activity naturally emerges from learning, and the amount of persistent activity scales with the degree of manipulation required. These results shed insight into the current debate on WM encoding and suggest that persistent activity can vary markedly between short-term memory tasks with different cognitive demands.