AirPods Max won't complete pairing sequence

My AirPod Max stopped connecting, and after reading the online help, I ended up doing a hard reset on the device. When I have it in pairing mode (i.e., flashing white), I see the setup animation (30% of the time), and tap "Connect". I then get the "Press and hold button for 5 seconds" prompt. At this point, holding down the button doesn't progress the connect sequence, but simply times out. When the white light stops flashing, and I hold the control button down, the I get solid white light for 3-4 seconds, and on releasing the button, I get a green light. Any ideas?