Dear M Gardner,
Did you have a look at
http://docs.moodle.org/en/Backup_FAQ
?
There is one problem in there that is particularly relevant to the upgrade from 1.5 to 1.6 "Restoring pre 1.6 non-ISO-8859-1 backups to Moodle 1.6 - Unicode," but if it were an encoding problem it would probably not be intermittent.
For me the most common problem is memory running out,and this may be more likely to occur in 1.6 since the functionality and number of options of moodle is increasing, and thus the memory required to perform a backup storing all these options is probably increasing likewise.
I recommend using non php zipping and unzipping routines as is mentions in the FAQ by setting the zip and unzip variables in Admin settings (http://yoursite/moodle/admin/config.php)
which are on my computer
/usr/local/bin/zip
/usr/local/bin/unzip
That solves the problem for me since these programs use radically less memory than using php to perform the same task.
Other than that you can try and reduce the amount of memory/time used by backup by..
If you are using only a limited subset of modules, you might also try turning some of the off on the admin modules page.
Or if you do not need course files or user files or messages (etc.) you can control what you want to be backed up on the admin backup page.
If you can't cut the above, then if you have access to your server then consister increasing
max_execution_time
in php.ini.
Tim