I would say that resolving this issue will require some analysis of which files are missing.
It is most likely that the name lengths of the lost files is the problem. CD-ROM file systems have not evolved to match the flexibility of the Windows FAT32/NTFS file systems. Given the current standard in CD-ROM file systems, I think you will find that no CD-ROM writing software can support “long” file names.
Message Saver does a file existence check when it saves each message. If you specify a subject length limit, the existence check will honour the limit. In addition, Message Saver ensures that a sequence of messages with the same subject will be preserved (with a distinct file name for each message). However, when copying from hard drive to CD-ROM the truncation may, as you suspect, cause the distinctness to be lost and files to be overwritten.
I would suggest that you investigate the maximum allowed file name length (it may vary depending on the directory depth). Then specify an appropriate subject length limit in Message Saver, taking into account that up to 11 additional characters will be required for the suffix. Then the distinct file names created can be copied unchanged to CD-ROM.
I hope this helps.