Thread referenced kinda old and it did have mulitple causes and solutions per situation ... nothing universal that I saw ... soooo ....
Besides the debug output can you find any hints in error log of web service or any references in php error logs?
A few things to check ... amount a memory a php script can consume, max time a php script can run, number of files opened (backups containing scorms do have multiple files), a plugin/addon that was compatible in 2.8 but no longer compatible in 3.2.
Are you stepping through the backup process or using the 'skip to end' button? One of the comments in the files referenced in the debug says to throw that error if the 'backup plan isn't correct' ... plan to backup is created in stages, I think .. maybe one of those skipped.
Have command line access? If so, could use the moodlecode/admin/cli/backup.php script from the command line to backup the course. Takes apache/web service out of the loop in backups and think I'd send the backup to a known location so if it does succeed backup can be found and it it has a humanly recognizable name. Plus, if restore becomes and issue that backup can be inspected via command line as well.
'spirit of sharing', Ken