How can I filter this listview and keep my selections?

Question

So I've got the following code setup to present a list of items that are imported from an XML file. The user makes selections and then exports their choices to XML. Selecting multiple lines works fine, but if the filter at the top is used, it will uncheck all the existing selections. Not sure if I need to filter it differently or if there's a property that will hold those values. The script is PowerShell and has a XAML file as well.

Powershell search function (filter):
$syncHash.WPFtb_Search.Add_TextChanged( { $syncHash.WPFlv_xml.ItemsSource = $arr.Where( { $_.Acc_Unit -like "*$($syncHash.WPFtb_search.Text)*" } ) } )

XAML:
`<Window x:Class="O365DGMembers.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:local="clr-namespace:O365DGMembers"
xmlns:dxg="http://schemas.devexpress.com/winfx/2008/xaml/grid"
mc:Ignorable="d"
Title="Company Selector" Height="600" Width="710" ResizeMode="CanMinimize" SizeToContent="Width" WindowStartupLocation="CenterScreen">

<Grid Name="maingrid">  
    <Grid.RowDefinitions>  
        <RowDefinition Height="1.5*"></RowDefinition>  
        <RowDefinition Height="10*"></RowDefinition>  
    </Grid.RowDefinitions>  
    <Grid.ColumnDefinitions>  
        <ColumnDefinition Width="*"></ColumnDefinition>  
        <ColumnDefinition Width="*"></ColumnDefinition>  
        <ColumnDefinition Width="*"></ColumnDefinition>  
    </Grid.ColumnDefinitions>  


    <StackPanel Grid.Column="0" FlowDirection="LeftToRight" Grid.Row="0" Height="30" Orientation="Horizontal">  
        <Label Content="Filter :" HorizontalAlignment="Center" Margin="2,2,2,2" Width="60" Height="25" HorizontalContentAlignment="Center" VerticalContentAlignment="Center"/>  
        <TextBox Name ="tb_search" HorizontalAlignment="Center" Height="25" Width="150" Margin="2,2,2,2" HorizontalContentAlignment="Center" VerticalContentAlignment="Center"></TextBox>  
    </StackPanel>  
    <Button Name="btn_export" Content="Export Selection" Grid.Column="2" HorizontalAlignment="Stretch" Margin="20,2,2,2" FontSize="11" Height="25" Width="100" VerticalContentAlignment="Center"></Button>  
    <ListView Name="lv_xml" Grid.Row="1" Grid.ColumnSpan="3" SelectedValue="{Binding ElementName=cbox_resp, Path=SelectedValue, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" IsSynchronizedWithCurrentItem="False" SelectionMode="Multiple">  
        <ListView.View>  
            <GridView>  
                <GridViewColumn Header="Select">  
                    <GridViewColumn.CellTemplate>  
                        <DataTemplate>  
                            <StackPanel Orientation="Horizontal">  
                                <CheckBox Tag="{Binding IsChecked}" IsChecked="{Binding RelativeSource={RelativeSource AncestorType={x:Type ListViewItem}}, Path=IsSelected}" />  
                            </StackPanel>  
                        </DataTemplate>  
                    </GridViewColumn.CellTemplate>  
                </GridViewColumn>  
                <GridViewColumn Header="Company" Width="60" DisplayMemberBinding="{Binding Company}"/>  
                <GridViewColumn Header="Company Description" Width="150" DisplayMemberBinding="{Binding CompanyName}"/>  
                <GridViewColumn Header="Acc__Unit" Width="65" DisplayMemberBinding="{Binding 'Acc_Unit'}"></GridViewColumn>  
                <GridViewColumn Header="Description" Width="250" DisplayMemberBinding="{Binding 'Acc_UnitDescription'}"></GridViewColumn>  
                <GridViewColumn Header="Primary Reporting" Width="110">  
                    <GridViewColumn.CellTemplate>  
                        <DataTemplate>  
                            <ComboBox Name="cb_resp" Width="60" HorizontalAlignment="Stretch" HorizontalContentAlignment="Center" SelectedItem="{Binding Path=Preporting, Mode=TwoWay}">  
                                <ComboBoxItem IsSelected="True">TRUE</ComboBoxItem>  
                                <ComboBoxItem>FALSE</ComboBoxItem>  
                            </ComboBox>  
                        </DataTemplate>  
                    </GridViewColumn.CellTemplate>  
                </GridViewColumn>  
                <GridViewColumn Header="Responsibility" Width="150">  
                    <GridViewColumn.CellTemplate>  
                        <DataTemplate>  
                            <ComboBox Name="cbox_resp" HorizontalAlignment="Stretch" HorizontalContentAlignment="Center" SelectedItem="{Binding Path=Resp, Mode=TwoWay}">  
                                <ComboBoxItem>Executive Director</ComboBoxItem>  
                                <ComboBoxItem>Vice President</ComboBoxItem>  
                                <ComboBoxItem IsSelected="True">Productivity</ComboBoxItem>  
                                <ComboBoxItem>Director</ComboBoxItem>  
                                <ComboBoxItem>Manager</ComboBoxItem>  
                                <ComboBoxItem>Budget</ComboBoxItem>  
                            </ComboBox>  
                        </DataTemplate>  
                    </GridViewColumn.CellTemplate>  
                </GridViewColumn>  
              
            </GridView>  
              
        </ListView.View>  
        <ListView.Resources>  
            <Style TargetType="ListViewItem">  
                <Setter Property="HorizontalContentAlignment" Value="Stretch" />  
            </Style>  
        </ListView.Resources>  
    </ListView>  
</Grid>  

</Window>`

Any ideas?