I'm having the same issue which I described in the thread "Log shipping restore job doesn't restore"
Interestingly, this is also not standard SQL Log Shipping. The log files originate on an Internet-facing domain and are passed through a firewall via an FTP job to a server in a secure domain.
Oddly there are five databases on the Internet-facing instance that send their log files through the firewall to the same target instance, and four of the restore jobs work - one doesn't.
If anyone has figured this out please let us know.