@Somnus, thanks for replying. Yes, I've contacted support to investigate the issue, but I agree it's likely a hardware problem. For completeness' sake, here's what I'm seeing in the controller for that EAP:

But for a functioning EAP, here's what I see:

And from SSH, I only see eth0, lo, and br0:
/bin $ ifconfig
br0 Link encap:Ethernet HWaddr B0:A7:B9:XX:XX:XX
inet addr:10.0.0.6 Bcast:10.255.255.255 Mask:255.0.0.0
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:1872733 errors:0 dropped:819177 overruns:0 frame:0
TX packets:12634 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:386969934 (369.0 MiB) TX bytes:3779997 (3.6 MiB)
eth0 Link encap:Ethernet HWaddr B0:A7:B9:XX:XX:XX
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:1876806 errors:0 dropped:2078 overruns:0 frame:0
TX packets:12638 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:414423493 (395.2 MiB) TX bytes:4029571 (3.8 MiB)
Interrupt:10
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
UP LOOPBACK RUNNING MTU:65536 Metric:1
RX packets:4 errors:0 dropped:0 overruns:0 frame:0
TX packets:4 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1
RX bytes:360 (360.0 B) TX bytes:360 (360.0 B)
But from a functioning EAP, I see:
/bin $ ifconfig
br0 Link encap:Ethernet HWaddr B0:A7:XX:XX:XX
inet addr:10.0.0.7 Bcast:10.255.255.255 Mask:255.0.0.0
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:2110108 errors:0 dropped:909376 overruns:0 frame:0
TX packets:19041 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:426630307 (406.8 MiB) TX bytes:8155882 (7.7 MiB)
eth0 Link encap:Ethernet HWaddr B0:A7:B9:XX:XX:XX
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:20294940 errors:0 dropped:2211 overruns:0 frame:0
TX packets:24675505 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:11007771692 (10.2 GiB) TX bytes:11609301320 (10.8 GiB)
Interrupt:10
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
UP LOOPBACK RUNNING MTU:65536 Metric:1
RX packets:4 errors:0 dropped:0 overruns:0 frame:0
TX packets:4 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1
RX bytes:360 (360.0 B) TX bytes:360 (360.0 B)
ra0 Link encap:Ethernet HWaddr B0:A7:B9:XX:XX:XX
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:94627 errors:32616 dropped:32616 overruns:0 frame:0
TX packets:73151 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:13751731 (13.1 MiB) TX bytes:43993236 (41.9 MiB)
Interrupt:31
rax0 Link encap:Ethernet HWaddr B0:A7:B9:XX:XX:XX
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:24951181 errors:371313 dropped:371313 overruns:0 frame:0
TX packets:18195593 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:2911865839 (2.7 GiB) TX bytes:1950468022 (1.8 GiB)
Hope this helps someone else identify this issue.