The wiper arms are indeed a weak point , either the blade flies off the arm (worst case the arm scratches the windscreen) or the whole unit comes off the spindle (tends to do less damage)
By stopping in time you have probably saved windscreen damage (but got rather wetter in the process!) You can drill the arm to take a small nut and bolt , or bend the tags on the arm with pliers to get a more positive fixing , but by far the best solution is to use some of the newly made up wiper blades done by an enthusiast on this forum (Cooperman?) they are brilliant and don't have the fantastic drag on the factory units so they won't fly off.