Forcing a WPF tooltip to stay on the screen

If you want to set this for just one tooltip, set the duration on the object having the Tooltip, like this:

<Label ToolTipService.ShowDuration="12000" Name="lblShowTooltip" Content="Shows tooltip">
    <Label.ToolTip>
        <ToolTip>
            <TextBlock>Hello world!</TextBlock>
        </ToolTip>
    </Label.ToolTip>
</Label>

I’d say that this design was chosen because it allows same tooltip with different timeouts on different controls.

If you want this globally for your whole app, see the accepted answer.