That's not a valid network configuration except in a very few specialized rare instances.I think I've finally solved this problem. I changed the default gateway setting to match the IP address of the Apex. It's been working for about 14 days with no restarts.
Unless there is something really weird going on in the firmware, with the default gateway and the IP address set to the same value, you won't be able to get remote access via the Internet, and the controller will not be able to send emails.