kernel 2.6.32-431.el6.x86_64 e1000e eth0 reset adapter unexpectedly

Issue

One of our servers, test.redhat.com, loses network connectivity shortly after
booting up under kernel 2.6.32-431.el6.x86_64 and 2.6.32-431.3.1.el6.x86_64.
From /var/log/messages:

Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): carrier is ON
Jan  8 12:22:57 test kernel: 802.1Q VLAN Support v1.8 Ben Greear <one@example.com>
Jan  8 12:22:57 test kernel: All bugs added by David S. Miller <xyz@redhat.com>
Jan  8 12:22:57 test kernel: 8021q: adding VLAN 0 to HW filter on device eth0
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): new Ethernet device (driver: 'e1000e' ifindex: 2)
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): exported as /org/freedesktop/NetworkManager/Devices/0
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): now managed
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): device state change: 1 -> 2 (reason 41)
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): preparing device.
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) starting connection 'System eth0'
Jan  8 12:22:57 test NetworkManager[6287]: (nm-device.c:3304):nm_device_activate: runtime check failed: (priv->state == NM_DEVICE_STATE_DISCONNECTED)
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): device state change: 2 -> 7 (reason 0)
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 3 of 5 (IP Configure Start) scheduled.
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): carrier is OFF
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): new Ethernet device (driver: 'e1000e' ifindex: 3)
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): exported as /org/freedesktop/NetworkManager/Devices/1
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): now managed
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): device state change: 1 -> 2 (reason 2)
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): bringing up device.
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): preparing device.
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth1): deactivating device (reason: 2).
Jan  8 12:22:57 test kernel: ADDRCONF(NETDEV_UP): eth1: link is not ready
Jan  8 12:22:57 test kernel: 8021q: adding VLAN 0 to HW filter on device eth1
Jan  8 12:22:57 test NetworkManager[6287]: <info> modem-manager is now available
Jan  8 12:22:57 test NetworkManager[6287]: <info> Trying to start the supplicant...
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 3 of 5 (IP Configure Start) started...
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 4 of 5 (IP4 Configure Get) scheduled...
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 3 of 5 (IP Configure Start) complete.
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 4 of 5 (IP4 Configure Get) started...
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 5 of 5 (IP Configure Commit) scheduled...
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 4 of 5 (IP4 Configure Get) complete.
Jan  8 12:22:57 test NetworkManager[6287]: <info> Activation (eth0) Stage 5 of 5 (IP Configure Commit) started...
Jan  8 12:22:57 test NetworkManager[6287]: <info> (eth0): device state change: 7 -> 8 (reason 0)
Jan  8 12:22:58 test NetworkManager[6287]: <info> Policy set 'System eth0' (eth0) as default for IPv4 routing and DNS.
Jan  8 12:22:58 test NetworkManager[6287]: <info> Activation (eth0) successful, device activated.
Jan  8 12:22:58 test NetworkManager[6287]: <info> Activation (eth0) Stage 5 of 5 (IP Configure Commit) complete.
Jan  8 12:22:58 test NetworkManager[6287]: <info> wpa_supplicant started