Stuff: If you are not strong enough (Strength = 45) than your agility will drop because you cannot wield the weapon as well and you become less agile using the larger weapon. DD will allow you to equip items that are above your strength, level or agility but it will cause a stat loss until you meet all the requirements for the item. If your strength is not at 45 you will lose agility.
If you are strong enough to use the weapon then it sounds like you had something that was adding some artificial agility or strength.
Check the weapon you replaced with the Singing Blade for charms or magic that would add to your agility or strength. Easiest way it to un-equip it and see if your agility or strength drops. Also if you equipped any new armor items, at the same time, that might have replaced armor that was adding agility / strength points.
If your old weapon / armor was adding agility or strength, unequipping would cause your agility to be lower by the number of points added. If your strength is less than 45 your agility would also drop.
Edit: Also there are weapons / armor / amulets / rings etc that are cursed. If you equip cursed items certain stats will drop but . . . cursed items usually drop stats by a large amount (depending on the item). A weapon may have large damage points but give a -20 to stamina for example.