Had this before Christmas with BAH. Tried to call a few times and got cut off as “too busy”.
Ended up on webchat where the agent told me it had failed and the payment would eventually drop off my Amex after a few days.
When I said payment was due in couple of days for holiday and the failed payment had taken up thousands of my credit limit they suggested contacting Amex to up my credit limit so I could try to make the payment again….
Of course when I tried again just to pay £10 it failed so I rang up and eventually got through to someone who took payment over the phone telling me “that happens all the time”.