A StackPanel essentially creates an area with an infinite amount of space along its orietnation axix; a horizontal stack layout will have unlimited width thus not need to wrap the text.
The layout you want can instead be achieved with a DockPanel:
<App Theme="Basic">
<ScrollView>
<StackPanel>
<DockPanel>
<Image Dock="Left" File="Assets/background1.png" Width="100"
StretchMode="UniformToFill"/>
<StackPanel>
<Text FontSize="15" TextColor="#333" Value="Edwin Reynoso" />
<Text FontSize="15" TextColor="#aaa" Value="10:00AM" />
<Text TextWrapping="Wrap" Value="Lorem ipsum dolor sit amet, consectetur adipisicing elit. Recusandae, numquam nulla eveniet quia perspiciatis ab autem temporibus harum voluptatibus nostrum, maiores reiciendis! Sunt adipisci vel, architecto, similique minus totam! Pariatur?" />
</StackPanel>
</DockPanel>
</StackPanel>
</ScrollView>
</App>
The DockPanel lets you place things at the various edges of a region but still use the natural sizing of the content and limit it to the maximums of the parent container.