We resolved this a while back, but I figured I'd post the solution for everyone else's benefit. When the button to upgrade appeared, site wouldn't update to UNA 12.
Suggested fix was to switch to php5.6 and to use cron job.
/opt/alt/php56/usr/bin/php -q /home/path_to_site/periodic/cron.php
It's important to note that while this might work for UNA hosted sites, for TMD hosted sites, the php path is different.
Correct path and cronjob for TMD hosted sites (dedicated server, at least) is
|/usr/local/bin/ea-php56 -q /home/path_to_site/periodic/cron.php|
Also, after upgrading, you need to switch the PHP version back.