I have opened a case with support (#00607680) and they have confirmed that this is a limitation of the product. Looking at the log file produced (C:\ProgramData\Veeam\Backup\<job name>\Job.<job name>.FileCopy.log) we can see the following error:
It would be very helpful to have support added for this in future releases.[24.07.2014 13:37:06] <01> Error The specified path, file name, or both are too long. The fully qualified file name must be less than 260 characters, and the directory name must be less than 248 characters. at System.IO.PathHelper.GetFullPathName()
[24.07.2014 13:37:06] <01> Error at System.IO.Path.NormalizePath(String path, Boolean fullCheck, Int32 maxPathLength, Boolean expandShortPaths)
[24.07.2014 13:37:06] <01> Error at System.Security.Util.StringExpressionSet.CanonicalizePath(String path, Boolean needFullPath)
[24.07.2014 13:37:06] <01> Error at System.Security.Util.StringExpressionSet.CreateListFromExpressions(String[] str, Boolean needFullPath)
[24.07.2014 13:37:06] <01> Error at System.Security.Permissions.FileIOPermission.AddPathList(FileIOPermissionAccess access, AccessControlActions control, String[] pathListOrig, Boolean checkForDuplicates, Boolean needFullPath, Boolean copyPathList)
[24.07.2014 13:37:06] <01> Error at System.IO.FileSystemInfo.get_FullName()