When tabbing from first PanelBar to the second one it neither passes through the contentTemplate elements, nor to the second panelbar:
 
<telerik:RadPanelBar runat="server" ID="radPnlBarFundingSources" Width="100%" ExpandMode="MultipleExpandedItems" TabIndex="1">
            <Items>
                <telerik:RadPanelItem runat="server" Text="Funding Source">
                    <ContentTemplate>
                        <telerik:RadListBox runat="server" ID="radLbAvailFundingSource" Height="100px" Width="40%" SelectionMode="Multiple" AllowTransfer="true" TransferMode="Move" AllowTransferOnDoubleClick="true" TransferToID="radLbSelFundingSource" ButtonSettings-AreaWidth="35px" Enabled="True" style="font-family: Verdana, Trebuchet MS,Arial,sans-serif; font-size:0.9em;"></telerik:RadListBox>
                        <telerik:RadListBox runat="server" ID="radLbSelFundingSource" Height="100px" Width="40%"></telerik:RadListBox>
                    </ContentTemplate>
                </telerik:RadPanelItem>
            </Items>
        </telerik:RadPanelBar>
    </div>
    <div class="Row">
        <telerik:RadPanelBar runat="server" ID="radPnlBarContracts" Width="100%" TabIndex="2">
            <Items>
                 <telerik:RadPanelItem runat="server" Text="Contract">
                    <ContentTemplate>
                        <telerik:RadListBox runat="server" ID="radLbAvailContract" Height="100px" Width="40%" SelectionMode="Multiple" AllowTransfer="true" AllowTransferOnDoubleClick="true" TransferToID="radLbSelContract"  AutButtonSettings-AreaWidth="35px"></telerik:RadListBox>
                        <telerik:RadListBox runat="server" ID="radLbSelContract" Height="100px" Width="40%"></telerik:RadListBox>
                    </ContentTemplate>
                 </telerik:RadPanelItem>
            </Items>
        </telerik:RadPanelBar>

You should, in general, use the ContentTemplate to provide content to items.

By original design and old documentation, the ItemTemplate must not be collapsible at all, but since it has been for ages, we must fix that to avoid a breaking change.

Items that have an ItemTemplate have the following collapse/expand issues:

    - they require two clicks to collapse for the first time
    - setting Expanded=false on the server keeps the ItemTemplate expanded
    - until you click their header they do not heave the coloring and expand/collapse arrow

See this changeset on how the templates should work and the change from the previous descriptions: https://github.com/telerik/ajax-docs/commit/67f0a252ff24e2397e042fe5797de3610a75221d which is available in the following article http://docs.telerik.com/devtools/aspnet-ajax/controls/panelbar/templates/overview