The configurations of the three sites are identical, so I assumed it was a permission problem. I tried to run the backup from the command line while logged in as root, or nobody, or a regular user, and I had inconsistent results. Sometimes it ran, sometimes not, and I could not see a pattern.
Finally, I changed the order in which the backups are performed, and I found that the one that runs first consistently fails, no matter which site it is, then the other two run fine. I was able to reproduce that from the CLI: the first try will fail; the next ones within a reasonable time (less than an hour, apparently) will run fine, even if it is the exact command, or are run as a different user or on a different site. I am not able to pinpoint the time interval after which it resets itself, or correlate it to time outs or cache retention values, so I do not know where to look next.
Perhaps this can help find a problem in the Dropbox interface or in Joomla! itself, perhaps it is still a problem with my server. Any suggestions would be appreciated.
I am running Akeeba 3.1.5 and Joomla! 1.5.22 on a CentOS VPS, with Apache 2.2, and PHP5.
Jacques