Whether one-shot interactions can stably sustain mutual cooperation if they are based on a minimal form of reputation building has been the subject of considerable debate. We show by mathematical modeling that the answer is positive if we assume an individual's social network evolves in time. In this case, a stable mixture of discriminating and undiscriminating altruists can be proof against invasion by defectors. This sheds light on current discussions about the merits of different types of moral assessment, an issue where theoretical arguments and experimental findings seem at odds.Unexpectedly, our approach also relates to the proverbial observation that people tend to become more tightfisted with age.