Unable to upgrade from Plesk 10.3.1 => 10.4.4

[KristianW]

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PRODUCT, VERSION, OPERATING SYSTEM, ARCHITECTURE

Parallels Plesk 10.3.1 / 10.4.4
Debian Linux
64bit

PROBLEM DESCRIPTION AND STEPS TO REPRODUCE
Attempting to upgrade to Plesk 10.4.4 using Plesk Control Panel => Tools & Utilities => Updates.

ACTUAL RESULT
Update fails with following log:

Installation started in background
Checking whether the package dependencies are resolved.
E: Unable to locate package pp10.13.4-bootstrapper
E: Couldn't find any package by regex 'pp10.13.4-bootstrapper'
E: Version '2.3.6-11081018' for 'libapache2-mod-fcgid-psa' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'libpam-plesk' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'plesk-base' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'plesk-core' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'plesk-l10n' was not found
E: Version '10.13.4-11110218' for 'plesk-skins' was not found
E: Version '10.4.4-debian6.0.build1013111102.18' for 'psa' was not found
E: Version '10.13.4-debian6.0.build1013111101.14' for 'psa-awstats-configurator' was not found
E: Version '10.13.4-debian6.0.build1013111102.14' for 'psa-locale-base-en-us' was not found
E: Version '3.7-debian6.0.build1013111101.14' for 'psa-logrotate' was not found
E: Version '2.0.0-debian6.0.build1013111101.14' for 'psa-mod-fcgid-configurator' was not found
E: Version '1.3.3e-debian6.0.build1013111101.14' for 'psa-proftpd' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-pylibplesk' was not found
E: Version '10.4.4-debian6.0.build1013111101.14' for 'psa-updates' was not found
E: Version '10.13.4-debian6.0.build1013111101.14' for 'psa-vhost' was not found
E: Version '3.11.0-111102.17' for 'psa-autoinstaller' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-migration-agents' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-migration-manager' was not found
E: Version '10.13.4-debian6.0.build1013111101.14' for 'psa-health-monitor' was not found
E: Version '4.9.1-11080119' for 'sw-collectd' was not found
E: Version '1.4.2-11080119' for 'sw-librrd' was not found
E: Version '1.4.2-11080119' for 'sw-rrdtool' was not found
E: Version '10.4.4-36793.11110312' for 'pp-sitebuilder' was not found
E: Version '10.4.4-36793.11110312' for 'pp-sitebuilder-default-templates' was not found
E: Version '10.4.4-36793.11110312' for 'pp-sitebuilder-skins' was not found
E: Version '1.6.1-debian6.0.build1013111101.14' for 'psa-php5-configurator' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'plesk-mail-qc-driver' was not found
E: Version '3.0.8-debian6.0.build1013111101.14' for 'psa-courier-imap' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-mail-driver-common' was not found
E: Version '2:1.03-debian6.0.build1013111101.14' for 'psa-qmail' was not found
E: Version '0.88-debian6.0.build1013111101.14' for 'psa-qmail-rblsmtpd' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-watchdog' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-mailman-configurator' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-drweb-configurator' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-spamassassin' was not found
E: Version '10.13.4-debian6.0.build1013111102.18' for 'psa-backup-manager' was not found
E: Version '1:2.1.1-1.11080119' for 'psa-ftputil' was not found
E: Unable to locate package psa-libxml-proxy
E: Version '3.3.10-debian6.0.build1013111101.14' for 'psa-horde' was not found
E: Version '4.3.9-debian6.0.build1013111101.14' for 'psa-imp' was not found
E: Version '1.2.5-debian6.0.build1013111101.14' for 'psa-ingo' was not found
E: Version '2.3.5-debian6.0.build1013111101.14' for 'psa-kronolith' was not found
E: Version '1.1.3-debian6.0.build1013110801.18' for 'psa-mimp' was not found
E: Version '2.2.4-debian6.0.build1013111101.14' for 'psa-mnemo' was not found
E: Version '3.1.3-debian6.0.build1013111101.14' for 'psa-passwd' was not found
E: Version '2.3.5-debian6.0.build1013111101.14' for 'psa-turba' was not found
E: Version '1:1.04-debian6.0.build1013111101.14' for 'psa-atmail' was not found
---X--- `apt-get` output ---------------------
Reading package lists...
Building dependency tree...
Reading state information...

---------------------- `apt-get` output ---X---
Collecting error details into log file...
Error: Installation will not continue
Not all packages were installed.
Please, contact product technical support.

EXPECTED RESULT
Plesk updates to 10.4.4 without any errors.

ANY ADDITIONAL INFORMATION
I have updated my similar Windows Server 2008 to Plesk 10.4.4 without issues.
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[KristianW]

Full Error Log

The full error log was about 5x too long, so I've uploaded it here (expires in 30 days).