Wow, that must have been a bit frightening!

Yes, like all things wireless, as most are more or less restricted by law to the same 2.4 GHz band, when things get very crowded it can quickly turn into a silent fight for bandwidth, and WiFi often wins (hopefully, nowadays WiFi is pushing towards the 5 GHz band and even other higher bands, so in time this will be less of a problem).
The best thing to do to avoid this kind of thing would be to pair the Sylphyo and Link again when beginning the sound check, making sure all the other wireless gear is on-stage too and active, so that the Sylphyo/Link will fail to pair in the more-crowded channels, and will naturally land into a less-crowded channel.