If virtual heritage is the application of virtual reality to cultural heritage, then one might assume that virtual heritage (and 3D digital heritage in general) successfully communicates the need to preserve the cultural significance of physical artefacts and intangible heritage. However, digital heritage models are seldom seen outside of conference presentations, one-off museum exhibitions, or digital reconstructions used in films and television programs. To understand why, we surveyed 1483 digital heritage papers published in 14 recent proceedings. Only 264 explicitly mentioned 3D models and related assets; 19 contained links, but none of these links worked. This is clearly not sustainable, neither for scholarly activity nor as a way to engage the public in heritage preservation. To encourage more sustainable research practices, 3D models must be actively promoted as scholarly resources. In this paper, we also recommend ways researchers could better sustain these 3D models and assets both as digital cultural artefacts and as tools to help the public explore the vital but often overlooked relationship between built heritage and the natural world.