I sent a trouble report to Blogger about students not being able to accept invitations, and here's the note I got back:
A Blogger invitation link will only work for one time and if it has
already been clicked on, you will need to use a new invite. If you are a
team member, we suggest that you request to be re-invited to the blog by
the blog's administrator. If you are an administrator, you should
reinvite the members of your blog so that they can accept the invitation.
If you continue to see problems, please try to log out of Blogger and shut
down your browser, then try to log in to Blogger once again.
Please see our Blogger Help article for further details:
http://help.blogger.com/bin/answer.py?answer=642&query=invite&topic=0&type=f
Thank you for using Blogger.
Blogger Support