No matter what I do, my Sophos Antivirus icon has a red "X" over it and when I hover my mouse over it a box pops-up that reads "Update has failed"

First, be assured that Sophos IS up to date. You can check this by opening Sophos (right-click the icon and choose "Open Sophos Antivirus"). The time of the latest successful update is listed in the upper-lefthand corner of the screen. This happens because Sophos Antivirus is configured to update from a college server first. This server is available on campus only. When Sophos fails to see this server, it will connect to the Sophos website and download the update.

Due to this unique configuration the icon will indicate that the update has failed even when Sophos was able to contact the secondary server.