In 2011, hydrogen peroxide (HOOH) was observed for the first time outside the solar system (Bergman et al., A&A, 2011, 531, L8). This detection appeared a posteriori quite natural, as HOOH is an intermediate product in the formation of water on the surface of dust grains. Following up on this detection, we present a search for HOOH in a diverse sample of sources in different environments, including low-mass protostars and regions with very high column densities, such as Infrared Dark Clouds (IRDCs). We do not detect the molecule in any other source than Oph A, and derive 3σ upper limits for the abundance of HOOH relative to H2 lower than in Oph A for most sources. This result sheds a different light on our understanding of the detection of HOOH in Oph A, and shifts the puzzle to why this source seems to be special. Therefore we rediscuss the detection of HOOH in Oph A, as well as the implications of the low abundance of HOOH, and its similarity with the case of O2. Our chemical models show that the production of HOOH is extremely sensitive to the temperature, and favored only in the range 20−30 K. The relatively high abundance of HOOH observed in Oph A suggests that the bulk of the material lies at a temperature in the range 20−30 K.