Assuming that you have gotten a GPS fix and that the time did not get corrected then the problem is either a corrupt or missing time zone file.
You can force an install of this file by deleting it from the Edge if it is there, Garmin\gmaptz.img. After removing it from the Edge switch the Edge on so that it can update the device.fit and GarminDevice.xml files.
Next, connect it back to the PC and run Garmin Express. It should offer up the install of the time zone map.
If it does not then let me know and I can post the file here and you can manually install it.
Try this. Rename to gmaptz.img
https://forums.garmin.com/cfs-file/__key/communityserver-discussions-components-files/150/3364.gmaptz.img
What region are you in and by how much is the time off by?
I suddenly relied something : the device is probably not getting any satellites . this is why the time is off by a weird diff. I mostly use it with no map just to track distance / HR / elevation etc. could it be that it is doing dead reckogning to provide me with this data ? I have a speed sensor attached.. I also noticed on my grain connect that I don't see the track on the map any more. Any idea on how to trouble shoot ? tried to toggle the GPS control on / off, select GPS only, GPS + GLONASS etc.. nothing helped :(