As far as I know, serious injuries primarily occur under two conditions:
1. The teacher is not properly qualified to be teaching aikido.
2. The student does not follow a qualified teacher's instructions.
P.S. Two of my students got serious injuries last semester; one broke his wrist and the other ruptured his Achilles tendon -- both got hurt playing basketball. (They watch too much NBA over here so they play too rough.) No aikido for those guys for quite some time and it really made me mad because they were my best uke.
(I told them not to play basketball ...)