It's not going to help much, but just as a comment:
This is a curious and unusual situation. If you can still contact the console from the outside then it suggests that the IP address hasn't changed (maybe it's on fixed IP anyway - I've lost track). If it were happening to a regular eg weekly schedule then maybe the network is resetting itself automatically for some reason as part of some routine housekeeping process, but is down for long enough to cause the logger to stop trying to upload packets to wl.com. It could, alternatively, be a firewall reset issue but if so I'm surprised that you can still get in from the outside.
Not suggesting that you attempt to try this, but purely as a speculation I do wonder whether if you had a little code utility that was able to send the NEWSETUP command to the console from the outside that this would reboot the console/logger. Never tried to use this command but its description reads like it might effectively trigger a reboot. Of course that's still not the same as a full power cycle, but it might conceivably be enough to do the trick.