Airport Extreme dropping out of network

I have a network of 3 Airport Extremes that all run the same network name and password. The are connected via ethernet throughout the building, and the primary one connects to the modem. The 2 secondary units operate in bridge mode to extend the wireless network.

I've started having an issue with one of the secondary units where it will "drop out" and lose its connection to the rest of the network. The light on the front still shows green, and my phone still sees a network being broadcasted, but it says "no internet connection" when I connect to it. Airport Utility doesn't see the unit anymore. I have to unplug the ethernet cable and plug it back in to get to work. This usually happens at least once a day. I've updated all the units to the latest firmware (7.7.9), but that apparently hasn't made any difference.

Are there any ideas as to what could be causing this?