This is an issue I've seen before.  The drop-down area of most drop-down controls is considered to be part of the "body" element and thus not in the row edit template, as far as the browser is concerned.  Once the user clicks on anything that isn't inside the row edit template, the template closes.

The workaround is to add some code to the grid's client-side BeforeRowTemplateClose event handler, to cancel the event whenever your WebCombo triggers the close.

function UltraWebGrid1_BeforeRowTemplateCloseHandler(gridName, rowId, bSaveChanges)
{
    var grid = igtbl_getGridById(gridName);
    var combo = igcmbo_getComboById("<%= WebCombo1.ClientID %>");
    var localEvent = (typeof(event)!='undefined') ? event : grid.event; 
    var localSrcElem = localEvent.srcElement ? localEvent.srcElement : localEvent.target;

    if (localEvent && localSrcElem && igtbl_contains(combo.container,localSrcElem))
        return true;
}