The preparatory attentional and memory processes theory (PAM) of prospective memory (PM) proposes that prospective remembering is influenced by the variation in the availability of WM resources. Consequently, PM should be impaired when WM resources are reduced either by direct WM manipulation or by individual differences associated with restricted WM performance. Our study tested this prediction in school-age children by examining the independent and interactive effects of three factors known to deplete availability of WM resources: increased processing demands of a concurrent arithmetic task, additional WM span requirements, and high trait anxiety. A sample of 10-year-old children (N = 128) performed a PM task, embedded in an ongoing arithmetic task, which progressively imposed greater WM processing demands. Half of these participants also concurrently carried out an embedded WM span task. The results supported the PAM hypothesis, showing that children’s PM was compromised by the restriction of WM resources, whether this resulted from increasing the processing demands on the ongoing task, from imposing additional WM span requirements, or from high trait anxiety. However, these WM-depleting factors exerted additive effects rather than an interactive impact, suggesting that they might each deplete different aspects of WM resource availability necessary for prospective remembering. Overall findings imply that children’s PM success is not only associated to their WM capacity but it mostly depends upon how many of those WM resources are available to be devoted to the PM requirement.