[Stooky Bill]

Is there not a fundamental problem with using a double lavalier mic to provide both primary and backup audio, in that if there’s a problem with one connection, such as damage, accidentally being unplugged, or not plugged in in the first place, the same issue is highly likely to affect the other?

Yes two mics isn't much good if there's not two of everything, right back to the sound desk.

The most likely thing to go wrong is the transmitter pack - have the batteries failed, has the presenter turned it off to have a wee?.....