Some schools have (overly) aggressive firewall protections and content filters in place -- especially on computers that students use -- whereas the security settings for teachers' computers are generally more lax. If the site is behaving differently for your students than it does for you, the school's security policy and/or firewall is likely to blame.
Here's a note from a school tech coordinator and how he resolved the issue:
"We have a firewall called CIPAFilter and students were able to get to the site but they couldn't upload their essays. So I went ahead and added www.essaytagger.com to the white list on the CIPAFilter for the students group and then it started working."
Essentially, your tech coordinator has to specify EssayTagger as a safe site for students to visit. These security measures are managed by each individual school and are out of our ability to control or influence. If you suspect that your school's security policy or firewall is causing problems, you'll have to raise the issue with your tech coordinator.