Kevin,
I regret to say it, but I suspect that your hard drive is dying. There may be I/O errors in QRecall's log, and you're welcome to send a diagnostic report, but from what you describe it would appear that your hard drive is encountering read failures when trying to read certain regions of the platter—specifically, those that the QRecall archive occupies.
When I test it with the Disk Utility or with Disk Warrior, they tell me the disk is okay ...
Disk Utility, Disk Warrior, and almost every other disk utility out there,
only validates the directory structure of the volume. They do not perform a comprehensive read/write test to confirm that all sectors of the drive are usable. You could lose a third of your drive, and Disk Utility will still report that it's fine. Any utility that reads the entire surface would require hours (and hours) to run. This is why QRecall's verify action takes as long as it does.
If you're interested in testing this theory, it's pretty easy from Terminal. You can run a simple command to read all of the data in the archive. If it's successful, it will finish after an hour or so. If there are I/O failures, the command should stop and spit out an error.
cat /Volumes/My3TBExternalVolName/pathtoarchive/ArchiveName.quanta/* > /dev/null && echo "No read problems"
Be patient. Even if it works, it will take a long time to finish. If the drive is encountering I/O failures, it will likely enter a retry/recalibrate cycle where it attempts to realign the heads and try again. Drives that are doing this run about 1,000 times slower than normal, so even if it hits an I/O error it could be many minutes before it's reported. You may hear the drive heads seek and clatter during this process. You can monitor the progress using Activity Monitor (switch to the Disk Activity tab) to see if it's still reading the drive or if the command has stalled. (Press Control-C in the Terminal window to kill the command.)
If you verify that it's I/O errors, you can attempt to recover the archive. You'll need a second volume with enough room to copy it. Choose the Repair Archive... command. Uncheck the "Use auto-repair information" option. (This is probably where your repair is getting stuck now.) Check the "Copy recovered content to new archive" and "Recover lost files" option.
This configuration will doggedly try to read every record in the original archive. Every record that can be read will be copied to the new archive. QRecall will then assemble the salvageable data into a usable archive. The "Recover lost files" option will collect orphaned files—files that don't belong to a folder because all of the folder information was lost—into a special "Recovered files" volume.
If the drive has a lot of damaged areas, the repair could run for days before it completes. So again, you'll need to be patient.