I've had a similar problem with LATAM, where booking a ticket on their Brazil website just wouldn't work and would give a nebulous "Your payment could not be completed for security reasons." I also ran into the document number issue, since I don't have a Brazilian CPF, so I think that's the root of the issue. Similar to you, my bank didn't even see the attempted charge. In my case, though, I switched to their US site and although being a few dollars more expensive, didn't require a document at the payment step.

Although typically people on FT advise against them, you may be better off booking through a reputable OTA which presumably wouldn't have the document restrictions.