He rules! Even if we don’t have a clue who he is?...

Is it true that, once a quorum has been established, it continues to exist no matter how many members leave during the course of the meeting?

No. Once a quorum at a meeting has been established, the continued presence of a quorum is presumed to exist only until the chair or any other member notices that a quorum is no longer present. If the chair notices the absence of a quorum, he or she should declare this fact, at least before taking any vote or stating the question on any new motion. Any member noticing the apparent absence of a quorum can and should make a Point of Order to that effect whenever another person is not speaking. It is dangerous to allow the transaction of substantive business to continue in the absence of a quorum. Although a Point of Order relating to the absence of a quorum is generally not permitted to affect prior action, if there is clear and convincing proof no quorum was present when business was transacted, the presiding officer can rule that business invalid (subject to appeal). [RONR (11th ed.), pp. 348-49; see also pp. 12-13 of RONRIB.]