Alright, I did some googling. I found a post
from another league owner:
The problem: Madden 13 connected careers has a glitch in which players never remain injured. Our league is affected by this glitch. So for example, you are playing a game and WR Calvin Johnson goes down with a torn ACL. After the game you notice he is out 8 weeks.....well when advance occurs, he will be back and free from injury. The glitch will occur when you start a connected career league with pre-existing injuries set to "off", which obviously we did because why would we choose otherwise. The only way this glitch does not happen is if the commish never changes any of the settings and owners never retire or recreate a coach. Unfortunately, we have already had owners retire and recreate coaches...so you will now notice that all teams are injury free at the start of every week. This glitch can not be reversed.
So according to that, just advancing can re-set injuries. Also owners retiring, changing settings, or who knows what else.
The only known fix for this glitch is to re-start the league
with pre-existing injuries turned off.