With very low air humidity, the voltage can stay for weeks but it usually decreases substantially overnight. Actually, any larger capacitor can store serious charges for quite a while. Big caps in power supplies can be much more dangerous than CRTs (lower voltage but much higher energy stored) - but better safe than sorry.
For discharging, don't use a plain screwdriver (resistance too low, so discharge is immediate) but rather an earthed (monitor chassis, water pipe or such) resistor of 1-100 kOhm to avoid damage or you getting startled.
PS: fixing bad solder points in HV areas is highly recommended rather than just slapping the monitor: I've had a case where the solder had already crawled along the arc gap and started to build a 'bridge' - ~2 millimeters - to a neighbor ground lead. The resulting short would probably have destroyed several components. :eek:
