What leads you to believe the updates were not being installed?
history.log file clearly shows unattended-upgrades running:
Start-Date: 2017-02-19 22:07:32
Commandline: /usr/bin/unattended-upgrade
Install: linux-headers-4.8.0-37:amd64 (4.8.0-37.39, automatic),
linux-signed-image-4.8.0-37-generic:amd64 (4.8.0-37.39, automatic),
linux-image-4.8.0-37-generic:amd64 (4.8.0-37.39, automatic),
linux-image-extra-4.8.0-37-generic:amd64 (4.8.0-37.39, automatic),
linux-headers-4.8.0-37-generic:amd64 (4.8.0-37.39, automatic)
Upgrade: libdns-export162:amd64 (1:9.10.3.dfsg.P4-10.1ubuntu1.1,
1:9.10.3.dfsg.P4-10.1ubuntu1.3), liboxideqt-qmlplugin:amd64
(1.19.4-0ubuntu0.16.10.1, 1.20.4-0ubuntu0.16.10.1), libavformat57:amd64
(7:3.0.5-0ubuntu0.16.10.1, 7:3.0.7-0ubuntu0.16.10.1), libavfilter6:amd64
(7:3.0.5-0ubuntu0.16.10.1, 7:3.0.7-0ubuntu0.16.10.1), libisccfg140:amd64
(1:9.10.3.dfsg.P4-10.1ubuntu1.1, 1:9.10.3.dfsg.P4-10.1ubuntu1.3),
liboxideqtquick0:amd64 (1.19.4-0ubuntu0.16.10.1, 1.20.4-0ubuntu0.16.10.1),
linux-headers-generic:amd64 (4.8.0.32.41, 4.8.0.37.46), libpcsclite1:amd64
(1.8.14-1ubuntu1, 1.8.14-1ubuntu1.16.10.1), linux-libc-dev:amd64 (4.8.0-32.34,
4.8.0-37.39), liboxideqtcore0:amd64 (1.19.4-0ubuntu0.16.10.1,
1.20.4-0ubuntu0.16.10.1), openssl:amd64 (1.0.2g-1ubuntu9, 1.0.2g-1ubuntu9.1),
libvncclient1:amd64 (0.9.10+dfsg-3build1, 0.9.10+dfsg-3ubuntu0.16.10.1),
libswresample2:amd64 (7:3.0.5-0ubuntu0.16.10.1, 7:3.0.7-0ubuntu0.16.10.1),
ntfs-3g:amd64 (1:2016.2.22AR.1-3, 1:2016.2.22AR.1-3ubuntu0.1), linux-ima
ge-generic:amd64 (4.8.0.32.41, 4.8.0.37.46), iucode-tool:amd64 (1.6.1-1,
1.6.1-1ubuntu0.1), bind9-host:amd64 (1:9.10.3.dfsg.P4-10.1ubuntu1.1,
1:9.10.3.dfsg.P4-10.1ubuntu1.3), linux-signed-image-generic:amd64 (4.8.0.32.41,
4.8.0.37.46), dnsutils:amd64 (1:9.10.3.dfsg.P4-10.1ubuntu1.1,
1:9.10.3.dfsg.P4-10.1ubuntu1.3), libisc160:amd64
(1:9.10.3.dfsg.P4-10.1ubuntu1.1, 1:9.10.3.dfsg.P4-10.1ubuntu1.3),
libxpm-dev:amd64 (1:3.5.11-1, 1:3.5.11-1ubuntu0.16.10.1),
flashplugin-installer:amd64 (24.0.0.186ubuntu0.16.10.1,
24.0.0.221ubuntu0.16.10.1), libntfs-3g871:amd64 (1:2016.2.22AR.1-3,
1:2016.2.22AR.1-3ubuntu0.1), linux-signed-generic:amd64 (4.8.0.32.41,
4.8.0.37.46), libpostproc54:amd64 (7:3.0.5-0ubuntu0.16.10.1,
7:3.0.7-0ubuntu0.16.10.1), thunderbird-gnome-support:amd64
(1:45.5.1+build1-0ubuntu0.16.10.1, 1:45.7.0+build1-0ubuntu0.16.10.1),
python-crypto:amd64 (2.6.1-6build1, 2.6.1-6ubuntu0.16.10.3),
libisc-export160:amd64 (1:9.10.3.dfsg.P4-10.1ubuntu1.1,
1:9.10.3.dfsg.P4-10.1ubuntu1.3), thunde
rbird-locale-en-us:amd64 (1:45.5.1+build1-0ubuntu0.16.10.1,
1:45.7.0+build1-0ubuntu0.16.10.1), firefox-locale-en:amd64
(50.1.0+build2-0ubuntu0.16.10.1, 51.0.1+build2-0ubuntu0.16.10.2),
liblwres141:amd64 (1:9.10.3.dfsg.P4-10.1ubuntu1.1,
1:9.10.3.dfsg.P4-10.1ubuntu1.3), libavcodec57:amd64 (7:3.0.5-0ubuntu0.16.10.1,
7:3.0.7-0ubuntu0.16.10.1), oxideqt-codecs-extra:amd64 (1.19.4-0ubuntu0.16.10.1,
1.20.4-0ubuntu0.16.10.1), libavutil55:amd64 (7:3.0.5-0ubuntu0.16.10.1,
7:3.0.7-0ubuntu0.16.10.1), libwebkit2gtk-4.0-37:amd64 (2.14.1-0ubuntu1,
2.14.5-0ubuntu0.16.10.1), libhogweed4:amd64 (3.2-1, 3.2-1ubuntu0.16.10.1),
libswscale4:amd64 (7:3.0.5-0ubuntu0.16.10.1, 7:3.0.7-0ubuntu0.16.10.1),
thunderbird:amd64 (1:45.5.1+build1-0ubuntu0.16.10.1,
1:45.7.0+build1-0ubuntu0.16.10.1), libdns162:amd64
(1:9.10.3.dfsg.P4-10.1ubuntu1.1, 1:9.10.3.dfsg.P4-10.1ubuntu1.3),
libnettle6:amd64 (3.2-1, 3.2-1ubuntu0.16.10.1), python3-crypto:amd64
(2.6.1-6build1, 2.6.1-6ubuntu0.16.10.3), gir1.2-webkit2-4.0:amd64 (2.14.1
-0ubuntu1, 2.14.5-0ubuntu0.16.10.1), libgnutls30:amd64 (3.5.3-5ubuntu1,
3.5.3-5ubuntu1.1), firefox:amd64 (50.1.0+build2-0ubuntu0.16.10.1,
51.0.1+build2-0ubuntu0.16.10.2), libisccc140:amd64
(1:9.10.3.dfsg.P4-10.1ubuntu1.1, 1:9.10.3.dfsg.P4-10.1ubuntu1.3),
libgc1c2:amd64 (1:7.4.2-8, 1:7.4.2-8ubuntu0.1), libjasper1:amd64
(1.900.1-debian1-2.4+deb8u1, 1.900.1-debian1-2.4+deb8u2build0.16.10.1),
libxpm4:amd64 (1:3.5.11-1, 1:3.5.11-1ubuntu0.16.10.1), libbind9-140:amd64
(1:9.10.3.dfsg.P4-10.1ubuntu1.1, 1:9.10.3.dfsg.P4-10.1ubuntu1.3),
libjavascriptcoregtk-4.0-18:amd64 (2.14.1-0ubuntu1, 2.14.5-0ubuntu0.16.10.1),
thunderbird-locale-en:amd64 (1:45.5.1+build1-0ubuntu0.16.10.1,
1:45.7.0+build1-0ubuntu0.16.10.1), linux-generic:amd64 (4.8.0.32.41,
4.8.0.37.46), libavresample3:amd64 (7:3.0.5-0ubuntu0.16.10.1,
7:3.0.7-0ubuntu0.16.10.1), libwebkit2gtk-4.0-37-gtk2:amd64 (2.14.1-0ubuntu1,
2.14.5-0ubuntu0.16.10.1), gir1.2-javascriptcoregtk-4.0:amd64 (2.14.1-0ubuntu1,
2.14.5-0ubuntu0.16.10.1), libssl1.0.0
:amd64 (1.0.2g-1ubuntu9, 1.0.2g-1ubuntu9.1)
End-Date: 2017-02-19 22:13:59
Start-Date: 2017-02-19 22:14:05
Commandline: /usr/bin/unattended-upgrade
Remove: linux-headers-4.8.0-22:amd64 (4.8.0-22.24),
linux-signed-image-4.8.0-22-generic:amd64 (4.8.0-22.24),
linux-image-4.8.0-22-generic:amd64 (4.8.0-22.24),
linux-image-extra-4.8.0-22-generic:amd64 (4.8.0-22.24),
linux-headers-4.8.0-22-generic:amd64 (4.8.0-22.24)