Cannot add more than 3 network cards to Hyper-V VM

When booting a Ubuntu 14.04 VM with 4 or more network cards, the following is shown in /var/log/kern.log:

Jan 30 12:00:26 hv-net-test kernel: [ 2.472973] hv_netvsc vmbus_11: Send section size: 6144, Section count:2560
Jan 30 12:00:26 hv-net-test kernel: [ 2.476599] hv_netvsc vmbus_11: Device MAC 00:15:5d:65:02:90 link state up
Jan 30 12:00:26 hv-net-test kernel: [ 2.486843] hv_netvsc: hv_netvsc channel opened successfully
Jan 30 12:00:26 hv-net-test kernel: [ 2.621152] hv_netvsc vmbus_13: Send section size: 6144, Section count:2560
Jan 30 12:00:26 hv-net-test kernel: [ 2.625926] hv_netvsc vmbus_13: Device MAC 00:15:5d:65:02:91 link state up
Jan 30 12:00:26 hv-net-test kernel: [ 2.627996] hv_netvsc: hv_netvsc channel opened successfully
Jan 30 12:00:26 hv-net-test kernel: [ 2.764902] hv_netvsc vmbus_14: Send section size: 6144, Section count:2560
Jan 30 12:00:26 hv-net-test kernel: [ 2.768815] hv_netvsc vmbus_14: Device MAC 00:15:5d:65:02:92 link state up
Jan 30 12:00:26 hv-net-test kernel: [ 2.770457] hv_netvsc: hv_netvsc channel opened successfully
Jan 30 12:00:26 hv-net-test kernel: [ 2.908398] hv_netvsc vmbus_15 (unnamed net_device) (uninitialized): Unable to complete send buffer initialization with NetVsp - status 2

The first 3 network devices are initialised successfully, but the 4th (and any subsequent devices - we've tested with up to 6 NICs) fail with the "status 2" error. This bug has been reproduced in the latest standard 14.04 kernel and the lts-xenial kernel packages.

Hyper-V platform is Windows Server 2012 (not 2012 R2). Hyper-V VM container is Generation 1 (Gen. 2 VM containers were introduced in 2012 R2). VM is configured with 4 (non-legacy) network interfaces.

The bug's symptoms are apparently identical to those described in this 2014 bug for Hyper-V on Windows Server 2008 R2: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=748609

As a guess, the fix for VMs running on 2008 R2 should probably also apply to VMs running on 2012...

ProblemType: Bug
DistroRelease: Ubuntu 14.04
Package: linux-image-4.4.0-31-generic 4.4.0-31.50~14.04.1
ProcVersionSignature: Ubuntu 4.4.0-31.50~14.04.1-generic 4.4.13
Uname: Linux 4.4.0-31-generic x86_64
ApportVersion: 2.14.1-0ubuntu3.23
Architecture: amd64
Date: Mon Jan 30 12:05:35 2017
InstallationDate: Installed on 2017-01-30 (0 days ago)
InstallationMedia: Ubuntu-Server 14.04.5 LTS "Trusty Tahr" - Release amd64 (20160803)
ProcEnviron:
 LANGUAGE=en_GB:en
 TERM=linux
 PATH=(custom, no user)
 LANG=en_GB.UTF-8
 SHELL=/bin/bash
SourcePackage: linux-lts-xenial
UpgradeStatus: No upgrade log present (probably fresh install)