I am assuming you are in AZ....hope the shops down there are good.
I have never heard of the TT or any of the 1.8T platforms having issues with dropping transmissions all of a sudden. I would think it is syncros for the 1st and 2nd gears. Those are made of brass I believe, and they are pretty soft compared to the other gear material, so they have a tendency to wear down or shave off. This happened to my Civic SI back in the day, but that was due to hard driving and slamming into second gear really hard...I only lost second gear.
Either that, or the shift selector rod that moves into the position of 1-2 has a problem, either cable, or shaft, not sure what linkage is where, but might be as simple as that. My MINI has occasional shift issues, well, not mine, but others. It is usually related to the cables from the shifter to the transmission.