The DropShadowEffect
doesn't disappear - it now applies to the whole rectangle.
This gives the desired effect:
<Border Background="Green">
<TextBlock Foreground="Black" Text="All Tasks">
<TextBlock.Effect>
<DropShadowEffect ShadowDepth="1.2"
Direction="270"
Opacity="0.6"
BlurRadius="1"
Color="Red"/>
</TextBlock.Effect>
</TextBlock>
</Border>