Files in ISO DIsappear When Mounted
ISO images typically contain more than one file system, the original ISO9660 file system for CD-ROMs (hence "ISO"), the "Joliet" extension to it for long filenames, and sometimes UDF or even a HFS+ file system. It's possible that one of them is corrupt, but the others are fine.

You could try explicitly mounting with the ISO9660 file system driver, as the UDF file system seems to be damaged. First, open a Terminal window. Attach the image without mounting:

hdiutil attach -nomount /path/to/image.iso


This should output the name of the disk device node, e.g.:

/dev/disk2


Create a mountpoint for the filesystem, e.g.

mkdir /Volumes/rescue


Then try mounting the device there, e.g.:

mount_cd9660 /dev/disk2 /Volumes/rescue


If it worked, it won't output anything, but the disk should be visible in Finder. (You can "eject" it via Finder when you're done)