DHCP is off on the apex and is set with a static local IP. I would think it has something to do with how often the apex rebroadcasts itself as it is still alive. Remember, I can access the wireless adapter after a power loss so I know it has connected sucessfully to the network. I can't access the apex though, even with local IP, unless I manually restart it, which somehow re-registers itslef back to the network.
Yes, I think I should plug the wireless adapter to the UPS.
I would have to assume it is the bridge.
Bridges can exhibit some very strange behavior.
If you had a power loss to all your computers, then when you went to ping/http access the Apex via it's IP address your computer is going to have to send out an ARP (broadcast) asking who has the IP address of the Apex and also ask it what is your MAC address.
All devices on the subnet get that request from your computer. The one that matches sends his MAC to your computer. From there, they can communicate via that Layer 2 MAC address.
If it happened again, I would see if just unplugging and plugging back in the Ethernet cable from the Apex to the bridge would help anything.