While the exact details of how credit cards process are a bit of a black box and each processor is different, there are a couple of common threads we see with most:
Visa and Mastercard always work but the processor has to flip switches to enable American Express and Discover Card and they often miss this initially and..
Their standard operating procedure is to react to almost any issue, including this one, by saying that it's a problem with your POS systems as a compulsory step one... ?
In some cases that may be true but in this case it's definitely not. We know this because you are approximately customer #1,000 that's experienced this issue. It happens often enough that some of the paperwork we send to the processors for account setup basically pleads with them to verify that your account is setup for AMEX and Discover to try to get in front of it. The good news, the fix appears to be easy once someone from the card processor is willing to investigate.
We don't mean to be brash, but the situation is a big frustration for everyone involved and we hope that this helps simplify matters. Additionally, we're not picking on a single processor. This is status quo and.. we get it, to a degree.
If you're a credit card processor reading this - please check the customer's account and confirm that Discover and American Express is enabled on their account (what some processors call "the build file"). Once this is updated no changes are needed to the credit card processing system - the end user can simply try one of these cards and confirm that it's working. If the test transaction doesn't work, escalate the matter inside your internal support team. If you do desire to engage us, and it turns out to be a setting on your end, the time involved will be billable to you - we'll need to get your approval and credit card on file before we proceed.
With any credit card processing change, you should always test, and settle the batch, and confirm that the batch settlement appears normal.