In September 2007 tardigrades became the first animal in the history to survive the combined effect of exposure to space vacuum, cosmic radiation, and ultra-violet 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 The main results from this experiment were reported in 2008, but some of the results have remained unpublished.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 no delayed effects of the exposure to space could be detected in the descendants (up to F3 generation) of space exposed Milnesium tardigradum. This indicates that individual tardigrades that survived the damage induced by environmental agents in space, and were able to reproduce, did not transfer any delayed 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 provide previously unreported data on two tardigrade species, Echiniscus testudo and Ramazzottius oberhaeuseri, that showed high survival after exposure to space vacuum and cosmic radiation within the TARDIS experiment.