LOTR: What happened to the dwarves in the Fourth Age?

Why was Moria a lost cause? The balrog was dead and orcs had lost their two main sponsors, and a fair portion of their population as well. Moria would have been ripe for recolonization.

It was apparently retaken by Durin VII, but I don’t know of anything more that was ever said about it.

[The Doctor] Dwarves! On a SPACESHIP! [/TD]

They got tossed.

I was thinking about this last night (yeah, I’m a Tolkien geek) and here’s my theory. Anyone who knows more about Tolkien’s stated views on the topic please let me know if this sounds right.

Up until Sauron was vanquished, the Valar still maintained a sort of covert influence in Middle-Earth, both directly and through the Maiar (Wizards). This accounted for a lot of the “marvels” and “magic” that existed then. After that, they pretty much left Middle-Earth to the men, and things got more humdrum. If this is true, then the Dwarves, being the creation of a Vala (Aule), would be expected to lose their vitality, and the giant eagles, presumably the beneficiaries of Manwe, dwindled to regular eagles. Any creatures that were Sauron’s, of course, would also lose vitality. The Elves mostly left Middle-Earth, and those who remained also dwindled; the Ents, originally awakened by the Elves, presumably died out or turned back into trees.