That sounds like a signal issue. When you press a button on your TV remote, a command is sent to a Cox server which then sends back a reply to the cable box. A poor signal can cause a slow response to remote commands and can even cause the cable box to lock up. It's possible there may not have been anything wrong with one or both of your first two cable boxes.
You should schedule a tech visit to check your signal strength. If your cable comes in from a pole, be sure to request the tech have a long ladder to enable the signal to be tested at the tap. If the tech determines you have a main line signal issue, he will notify Cox. They will escalate the issue to have a line technician research and make necessary corrections, at no cost to you.
Email cox.help@cox.com with your full name, the service address and a link to this thread.