scBroadcaster
There is a lot of stuff involved where the dropout can come from.
... we pick up the MADI signal (RJ45)
From where ?
Madi over RJ45 ? Maybe it is a AVB ?
...to then pass it on to the RME MADIface XT via coaxial cable.
A stereo analog signal ? Or a madi over BNC ?

I would start Fehlersuche by isolating the units.

Is the Madiface working together with the computer ? Can you listen music out of the computer on the headphone output of the Madiface ?

Is the FOH console working alone without dropouts ?
Why do you use this mio converter ? The soundcraft and the Madiface are already converters.
Why do you want to mix in the DAW when you have this incredible FOH console ?

...and how we can fix it?
I would reduce the set first.
kick the mio-converter out (überflüssig)!
All the microphones and instruments connect to the mixer.
From the mixer via madi to the Madiface.
Has your mixer the optional madi card ? It should.
Then you have all mic signals in the computer and can do the mix.
The loudspeakers are connected at the Madiface XLR main out.
You can record everything during the show and produce the audio for the video afterwards.
The Soundcraft mixer must have the madi connection board and the connection to the Madiface must work.
When the Madiface runs stable with the mac alone, then the dropouts should have been sorted out.

edit :
I was looking closer to that sonible thing, it seems to act as the madi-connection to the mixer.
I am sorry I was wrong.
Then you need it.
The official optional madi board would be better as it is made for the console and this sonible thing is still suspect to me.
Ouch ! I see the optional madi expansions card for this Soundcraft console is with RJ45 and USB only ! No optical no BNC, what a crap !
What I would do, get rid of the console and replace it with a Octamic XTC, stable madi connection via optical to the Madiface.
But anyway I highly recommend to do a test listening computer and Madiface only.

Haha ! The picture is outstanding with the band and the audience.
Very nice artwork.
Who did assemble this collection of devices ?
After all you let it be how it is and live with rare interrupts.
The proper Fehlersuche will take too much time by the numbers of candidates.
Each one must be connected solo to the Madiface and listen for hours and recording it.

But what you also can do, please take a look at the recordings. Is the interrupt visible in the wave ?
Did you record all mics seperate ?
Have all tracks the same gap ?
How exactly is the gap comparing each wave ?
Is this set new ?
Have you still Rückgabe-Frist or Umtausch-Möglichkeit ?
I would change the complete set.
Because, all that stuff from Soundcraft and also this ML-converter is in my opinion NOT MADI.
They say its madi but its not.
Those units use Hi-Q-Network to connect with ethernet cables, this is far away from madi.
You can try optical cables but I estimate no improvements.
Do you use more than 8 mics at the time ? I guess no.
Replace the whole Souncraft crap with one Octamic XTC and you are fine. And get about 4'000.- Fr back.
The livemix should be made with Totalmix (the way professional giant events do it).
The Youtube mix is also made by Totalmix it can be the same as for the in-house audience or it can be different, just in time.

From the product discription of the Sonible ML:MIO
MADI-Eingänge: 1x Twisted Pair (DiGiCo und Soundcraft kompatibel), 1x optisch (SC, 50/62.5µm Multimode), 1x koaxial (BNC 75 Ohm)
MADI-Ausgänge: 1x Twisted Pair (DiGiCo und Soundcraft kompatibel), 1x optisch (SC, 50/62.5µm multimode), 2x koaxial (BNC 75 Ohm)
RME compatible would be better.