You are not binding the ListPicker ItemTemplate. Bind it like this
<toolkit:ListPicker.ItemTemplate>
<DataTemplate>
<StackPanel Orientation="Horizontal">
<toolkit:PhoneTextBox Hint="firstname" Style="{StaticResource TransparentToolkitTextBoxStyle}" Text="{Binding FirstName}"/>
</StackPanel>
</DataTemplate>
</toolkit:ListPicker.ItemTemplate>
Make sure you are not setting any text box in OnNavigatedTo
method. if so your TextBox will reset again.
So, Do not Set any TextBox in that Method.