PSR B1259-63 is a binary system composed of a pulsar and a massive star. Weak gamma-ray emission was detected by the Fermi/LAT at the last periastron passage, unexpectedly followed 30 days later by a flare during which the flux was higher by a factor 10. This flare is a major puzzle for models of gamma-ray binaries. We propose a solution to this puzzle and explore its consequences for other gamma-ray binaries and on our understanding of pulsar winds.