Many species are poorly known, with the sum of our knowledge represented by specimens in museums. For assessment of conservation status the most enigmatic and challenging species are probably those known only from a single specimen. We examine the potential persistence of such species using the orchid flora of Madagascar as a case study. We apply a statistical method that tests the likelihood of species presence in relation to the time when a species was collected and a measure of annual collection effort, calculated in three ways based on specimen collection over time. The results suggest that as of 2000 up to nine of the 236 orchid species known from a single specimen may be inferred to be extinct under at least one of the three methods of estimating collection effort and extinction. In addition, up to two additional species are likely to be extinct by 2018 assuming no new collections were made by that time. Substantial collection effort and/or additional evidence will be needed to reach a decision on the persistence of more recently observed species known only from a single collection. This represents a challenge for conservation practitioners.