Update manager fills /boot until it blows up from insufficient disk space

[Charles]

Every few months, the update manager blows up trying to install a new kernel because it has filled the /boot partition with obsolete kernel images. The system isn't happy again until I manually remove old kernels, run update-grub, and get the updater to fix its botched kernel install. I use a separate boot partition due to an encrypted root, which I set up through the Ubuntu installer, so space is limited.

$ lsb_release -a
LSB Version: core-2.0-amd64:core-2.0-noarch:core-3.0-amd64:core-3.0-noarch:core-3.1-amd64:core-3.1-noarch:core-3.2-amd64:core-3.2-noarch:core-4.0-amd64:core-4.0-noarch:core-4.1-amd64:core-4.1-noarch:security-4.0-amd64:security-4.0-noarch:security-4.1-amd64:security-4.1-noarch
Distributor ID: Ubuntu
Description: Ubuntu 14.04.4 LTS
Release: 14.04
Codename: trusty

ProblemType: Bug
DistroRelease: Ubuntu 14.04
Package: update-manager 1:0.196.14
ProcVersionSignature: Ubuntu 3.13.0-85.129-generic 3.13.11-ckt36
Uname: Linux 3.13.0-85-generic x86_64
ApportVersion: 2.14.1-0ubuntu3.19
Architecture: amd64
CurrentDesktop: Unity
Date: Wed Apr 6 19:52:11 2016
DpkgHistoryLog.txt:
 Start-Date: 2016-04-06 19:35:16
 Commandline: aptdaemon role='role-commit-packages' sender=':1.59'
 Install: linux-image-extra-3.13.0-85-generic:amd64 (3.13.0-85.129), linux-image-3.13.0-85-generic:amd64 (3.13.0-85.129), linux-headers-3.13.0-85-generic:amd64 (3.13.0-85.129), linux-signed-image-3.13.0-85-generic:amd64 (3.13.0-85.129), linux-headers-3.13.0-85:amd64 (3.13.0-85.129)
 Upgrade: linux-headers-generic:amd64 (3.13.0.83.89, 3.13.0.85.91), linux-signed-generic:amd64 (3.13.0.83.89, 3.13.0.85.91), linux-signed-image-generic:amd64 (3.13.0.83.89, 3.13.0.85.91), xserver-xorg-video-openchrome:amd64 (0.3.3-1build1, 0.3.3-1ubuntu0.1), linux-libc-dev:amd64 (3.13.0-83.127, 3.13.0-85.129), libpcre3:amd64 (8.31-2ubuntu2.1, 8.31-2ubuntu2.2), linux-image-generic:amd64 (3.13.0.83.89, 3.13.0.85.91), linux-generic:amd64 (3.13.0.83.89, 3.13.0.85.91)
 End-Date: 2016-04-06 19:36:48
GsettingsChanges:
 b'com.ubuntu.update-manager' b'show-details' b'true'
 b'com.ubuntu.update-manager' b'first-run' b'false'
 b'com.ubuntu.update-manager' b'window-width' b'484'
 b'com.ubuntu.update-manager' b'launch-time' b'1459985458'
InstallationDate: Installed on 2014-08-02 (613 days ago)
InstallationMedia: Ubuntu 14.04.1 LTS "Trusty Tahr" - Release amd64 (20140722.2)
PackageArchitecture: all
ProcEnviron:
 LANGUAGE=en_US
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=en_US.UTF-8
 SHELL=/bin/bash
SourcePackage: update-manager
UpgradeStatus: No upgrade log present (probably fresh install)

[Jarno Suni (jarnos)]

How would you expect it to work?

[Launchpad Janitor (janitor)]

Status changed to 'Confirmed' because the bug affects multiple users.

[Jarno Suni (jarnos)]

Could you elaborate what do you mean by that update manager blows up? Do you mean you get a dialog like this https://i.stack.imgur.com/DppOi.png ?