I have a 25 year old wave radio. I get an intermittent loud pop when the radio is off. This occurs with no regularity. Maybe once or twice a week. Otherwise it works just like new.
It's great to hear your Wave radio has served you well! In regards to the pop noise, have you tried connecting the radio to a different power socket/outlet, to see if you notice any difference? If not, I'd recommend giving this a try to see if you notice the pop disappears or continues to happen.