Hi Cameron,
According to your description, all users are encountering regular disruption to connection using Outlook 15. If Outlook 15 can connect to servers normally when operating on other network, you are right that the issue may lie in the network environment.
Cameron, I suggest you check firewall whether it blocks TCP port 443.
Since our forum focuses on Office 365 for Business cloud service, we have limited resources or troubleshooting steps about Outlook client. As I know it, we have a dedicated support channel to deal with Outlook for Mac issue. I believe they will be more proper and professional to provide suggestions. Here is the link:
Microsoft Outlook Forum: http://answers.microsoft.com/en-us/mac/forum/macofficeo365
Best regards,
Chris Ni