Edited for the sake of future people with the same problem:
None of the troubleshooting steps that the Garmin reps suggest did anything. Checking date and time, turning off AV, rebooting, reinstalling, updating Express, even doing a master reset of the watch did not solve the problem.
The solution was to manually update the 225 firmware using a separate application, the Garmin Webupdater tool. Try that if you can't get your FT 225 to connect to the servers.