I don't know why the Pats have struggled, but I disagree with your assessment.
First, if the interior d-line is getting through the line, that takes away passing lanes and Brady has to adjust this throws which could send the pass off or poorly timed. Since right now two of the three starting interior o-linemen are out and the likely starter at the other position is playing out of position, this could be a significant problem over the last two days. An effective interior pass rush can wreck havoc on a QB even if rushers get nowhere near the QB.
Second, it is my understanding that if rusher gets to the QB (obviously not touching him) that the play is blown dead and automatically considered a sack. I haven't been to Patriots' camp in a few years. So Belichick might play through the sack, but it is pretty standard practice. Even so, if it is credited as a sack, the pass doesn't count.