Hello Sarah Walbridge,
Welcome to the community.
One thought would be to utilize a static background image in place of the Tableau Maps.
In addition, here is a list of the actions that cause the Tableau Online Maps to try to connect to the Internet and refresh:
We also supply a document to assist IT organizations with configuration of Proxy settings to allow for real time Map images: http://kb.tableausoftware.com/articles/knowledgebase/web-proxy-and-firewall-settings
Hope that helps.