I believe the problem is due to this mod OR because I restarted the lost tower mission too many times. After I beat the last gift quest all my soldiers' PCS slots are open, but they retained their bonuses, as shown in this pic:

http://steamcommunity.com/sharedfiles/filedetails/?id=730555924

As you can see she has kevlar armor and 11 HP, which is impossible to attain without a PCS, and her PCS slot is open.