The Dwarves are decaying because they reproduce slowly.
While Mark Olson does an excellent job at proving the Dwarves aren't "fading" he doesn't quite look at the text that inspired the question, so lets look at that closer.
The quote says the Noldor were preventing the decay of time that "only affected the Dwarves and the Eldar". While there is a mistake in this sentiment1, it's not that the Dwarves are decaying. The decay of the Dwarves has nothing to do with their power or interest in Middle-earth fading, but to do with the low reproduction rates and general lack of women in Dwarven populations. This caused the decay of the Dwarves in the later ages, they also became more secluded which is "why" we don't see them today.
Dís was the daughter of Thráin II. She is the only dwarf-woman named in these histories. It was said by Gimli that there are few dwarf-women, probably no more than a third of the whole people.
The Lord of the Rings - Appendix A, III: Durin's Folk
The number of dwarf-men that marry is actually less than one-third. For not all the women take husbands: some desire none; some desire one that they cannot get, and so will have no other. As for the men, very many also do not desire marriage, being engrossed in their crafts.
On top of the lack of Dwarven women, the population of Dwarves rarely rose quickly, this was because it was rare to see a Dwarf-woman bear up to 4 children. This low replacement ratio combined with the low amount of females marrying makes population growth and only happened in peace time in the recorded histories.
It is then said that Dwarves marry late, seldom before they are ninety or more,18 that they have few children (so many as four being rare)
History of Middle-earth - Volume XII: People's of Middle-earth, IX: The Making of Appendix A, (iv) Durin's Folk
You are right, Dwarves weren't permitted to sail the Straight-Road to Valinor. They were mortal and it is unclear what happens to them upon death. They believed they go to the Halls of Mandos to be cared for by Aule, but whether this is true is unclear.
1 It wasn't only the Eldar that faded but all Elves, while this is just a naming convention, the Eldar were only those that had seen the light of the two trees, the Calaquendi.