[Zigûr]

It might be worth considering the case of the Men of Duharrow also. Evidently the shades of dead men could linger long after their time, although in this case I'm not sure how long the society of the living Men of Dunharrow persisted before they entirely died out and were replaced by the spectres of the dead.

It seems to me that it was beyond the power of the Ainur to force the souls and bodies of mortals to stay united indefinitely, but the effect of the Rings seems to have circumvented this (albeit with obvious and severe side effects) by instead indefinitely extending the period of time in which the body and soul existed.

ie even the Ainur did not have the power to cause a mortal to "grow or obtain more life" beyond their span, but in Eä it was possible to, if you'll pardon the horrible sci-fi-ish-ness of the term, "warp" time in such a way that it produced "counterfeit immortality" at the price of corruption and great suffering on the part of the subject. This seems to be a different thing to directly counteracting the Gift of Men.

This seems to have been the normal state of affairs in places like Valinor where, in a sense, time passed and yet did not pass.