It sounds like they are being affected by the ‘max new accounts per registration ip’ Site Setting. The setting defaults to 3 new accounts. The setting’s description is:
If there are already (n) trust level 0 accounts from this IP (and none is a staff member or at TL2 or higher), stop accepting new signups from that IP.
You could try increasing the value of that setting. It seems possible that you have a lot of students access your forum from a single IP address.