Simply because the monster itself is no longer on the field:
From the UDE Specific Cards rulings:
"Skill Drain" does not stop you from activating Ignition Effects, but it does negate their effects as long as the Effect Monster remains on the field. If you Tribute "Cannon Soldier" to itself while "Skill Drain" is active, "Cannon Soldier"'s effect is not negated because "Cannon Soldier" is in the Graveyard, but if you Tribute a different monster for "Cannon Soldier"'s effect, then the effect is negated and your opponent takes no damage. Likewise, if you activate "Winged Minion"'s effect while "Skill Drain" is active, "Winged Minion" is no longer on the field and its effect resolves. If you activate "Exiled Force"'s effect while "Skill Drain" is active, "Exiled Force" is no longer on the field and you can select and destroy 1 monster on the field. If you Tribute "Paladin of White Dragon" to activate its effect while "Skill Drain" is active, it is no longer on the field and you can Special Summon "Blue-Eyes White Dragon". If you Tribute "Great Dezard" while "Skill Drain" is active, it is no longer on the field and you can Special Summon "Fushioh Richie".
Remember that the text of Skill Drain is:
"Card Text
Pay 1000 Life Points. As long as this card remains face-up on the field, negate the effects of all face-up Effect Monsters on the field. "
Note the face-up on the field, so if the monster is no longer on the field or is no longer face up (due to Book of Moon), then it's effect will resolve as normal.