I thought I did in the first three paragraphs, but I guess it wasn't clear enough: It depends on the attack.

Zoltraak? Mana depletion wins the encounter. The Barrier will not break, you just won't be able to produce them anymore and one will slip through.

"Modern" magical technique attacks that hit physically? Strong enough, and they will break the Barrier unless it has been reinforced, which slows down the activation time of the Barrier.