What's the input impedance of that amp? I wonder if it's a bit low for that CD player.Another thing I've seen a lot is mechanical connections causing those symptoms. They can almost seem like magic too; You'd think they'd be consistent but they're not. If the junction makes contact but poorly, it's an intermittent connection with highly changing resistance. Places it can develop are volume pots, switches and tube sockets.
Then there's those weird Valve Art tubes. Remember them on the Paramours? More magic. Sound great when running, but like Geiger counters when idle. Sometimes. And only every other tube does it, some sound great. Don't guess that's what's up with your amp, but I thought it worth mentioning. 'Spose it could be something like that.
Those are some of the things I'd look at.