Right now, he's not playing QB. He's lining up at the QB/WR/TE positions and playing very physical football, as a ball carrier, blocker, and pass catcher. The guys who play even one of these positions on the regular get banged up all the time.
When he actually plays QB, he's done a good job staying healthy, minus a freak thumb-to-the-helmet injury (which he courageously played through) and a lisfranc, which can happen to anyone at any time.