I duplicated the code you posted and it worked for me.
Any chance the event isn't actually wired up?
I built it two different ways and the event fired for me. How did you build it?
Also check to see if you somehow have an object covering the slider?
Version 1:
Open Blend 3, file>create project, Silverlight 3 Application + Website. Added a slider and named it (simply because you did). Added a label (to check the event firing).
Selected the component, switched over events and double-clicked the events for MouseLeftButtonDown and MouseLeftButtonUp to create the events and code-behind stubs. Updated the label when MouseLeftButtonUp fires.
Version 2: Open Blend 3, file>create project, Silverlight 3 Application + Website. Added a slider and a label. Right-clicked on the silverlight project in Blend and opened it in VS2008. Wired up the events in markup using intellisense.
Both version worked for me. Is this part of other code? If so try to make a version with just the slider and see if that works, if it does then something in your existing code may be off. I'll post my code so you can see it.
<UserControl
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:dataInput="clr-namespace:System.Windows.Controls;assembly=System.Windows.Controls.Data.Input"
x:Class="SilverlightAppSlider2Test.MainPage"
Width="640" Height="480">
<Grid x:Name="LayoutRoot" Background="White">
<Slider x:Name="sliderTime" MouseLeftButtonUp="Slider_MouseLeftButtonUp" MouseLeftButtonDown="sliderTime_MouseLeftButtonDown" Width="Auto" Height="20" Margin="5"/>
<dataInput:Label x:Name="Label1" Width="200"/>
</Grid>
</UserControl>
AND
private void Slider_MouseLeftButtonUp(object sender, System.Windows.Input.MouseButtonEventArgs e)
{
// TODO: Add event handler implementation here.
Label1.Content = "Mouse button left released.";
}