Since the Forerunner 405 does not have the Bluetooth hardware in order to sync with the Garmin Connect Mobile app, what you were likely seeing is that the watch was automatically syncing when in range of your computer. Once the activities are uploaded to Garmin Connect, they are visible in the Garmin Connect Mobile app.
Since the watch does not appear to be syncing you will want to troubleshoot syncing with your computer. Some basic recommendations would be to ensure that Garmin Express is up to date, the ANT Stick is being recognized by the computer, and that there isn't a file on the watch that may be corrupt and preventing a transfers.
You can reach out to Product Support for further assistance. Product Support contact information can be found at www.garmin.com/support.
