Yes, it is critically important to call sp_xml_removedocument. The statement in the article "This handle is valid for until the connection is reset, or until the execution of sp_xml_removedocument." is correct but does not mention the bug you ran into. If you do not call sp_xml_removedocument the handle is orphaned and will not be released. Overtime your handle count is going to increase and your server will eventually crash. (You can watch the handle count increase for sqlservr.exe by using the process tab of the task manager and adding the column for handles.)

Therefore our standard is to read the xml document into a temp table and immediately call sp_xml_removedocument before there is a chance to orphan the handle.