I've had monitors that would discharge themselves within seconds of killing the power. Others would hold a charge for hours. And the stubborn ones would usually build up charge again once discharged (after minutes), so be aware that you might have to discharge multiple times to fully "drain" it. Or, IOW, you might want to discharge again before trying to reconnect the anode lead.
Also, I just picked up a high-voltage probe--what a great tool! Not only can I use it for discharging, but it will tell me how much kilo-voltage the tube has (i.e., while running). If you can find these cheap, they're worth adding to your arcade tool collection IMHO.