Intermittently, the confirmation page on the fax says the fax failed (didn't go thru) but it actually did. Why is this? The confirmation page is printing false results, indicating the fax failed to go thru, when it actually went thru successfully on the receiving end. Why is this happening?

This is because some faxes don't have Error Correction Mode capabilities.

If there's a slight distortion on the line, the receiving machine (without ECM) receives a fax with some minor errors. And even though for a human eye the resulting fax page is perfectly readable, for the machine, that thinks only zeros and ones, there was an error detected in the data, and hence the trasmission failed.
Faxes with ECM when they detect an error, ask the sending fax to re-send the last portion of data, and this way can bring the transmission to a 100% successful end.

So the only thing you can do is ask your recipients to upgrade their fax machines to an ECM-capable model :)