Final answer:
The technology that likely encountered a failure is Near Field Communication (NFC) or a similar wireless payment system, which is used for mobile payments and requires close proximity between a phone and a payment device.
Step-by-step explanation:
The technology that failed to function properly in this scenario is most likely Near Field Communication (NFC) or a similar wireless payment technology. NFC is used in mobile payment systems and allows phones and payment devices to communicate when they are close to each other. If a customer's phone is not recognized by the payment processing device, it means there has been a failure in the interaction between the NFC chip in the phone and the payment terminal's NFC reader. This could be due to various reasons such as a malfunctioning NFC chip, a dead battery, the payment terminal being faulty or outdated, or even software-related issues on the phone or payment system.