In September 2007 tardigrades became the first animal in history to survive the combined effect of exposure to space vacuum, cosmic radiation and ultraviolet radiation in low Earth orbit. The main results from this experiment were reported in 2008, but some of the results have remained unpublished. Here we report that descendant generations of space-exposed tardigrades of the species Milnesium tardigradum did not show reduced performance. This indicates that individual tardigrades that survived the exposure to environmental extremes in space, and were able to reproduce, did not transfer any damage to later generations. Repair of environmentally induced damage may therefore follow a ‘make or break’ rule, such that a damaged animal either fails to repair all damage and dies, or repairs damage successfully and leaves no mutations to descendants. We also report that two additional tardigrade species, Echiniscus testudo and Ramazzottius oberhaeuseri, showed high survival after exposure to space vacuum and cosmic radiation within the TARDIS experiment.