Dwarves are biologically not viable (Tolkien nods again...)

"Dis" (Fili and Kili's mother) as imagined by Ancalinar - but I suspect she was (even-) less feminine than this, since Tolkien said dwarf-women were indistinguishable from the men. 

The Dwarves' numbers, although they sometimes flourished, often faced periods of decline, especially in periods of war. The slow increase of their population was due to the rarity of Dwarf-women, who made up only about a third of the total population. Dwarves seldom wedded before the age of ninety or more, and rarely had so many as four children. They took only one husband or wife in their lifetime, and were jealous, as in all matters of their rights. The number of Dwarf-men that married was actually less than half, for not all the Dwarf-women took husbands; some desired none, some wanted one they could not have and would have no other. Many Dwarf-men did not desire marriage because they were absorbed in their work. 

From Tolkien Gateway, summarizing the available 'canonical' information from the Appendices of Lord of the Rings and History of Middle Earth Volume 12.

JRR Tolkien clearly wanted his dwarves to be dedicated to their craft; and not interested in sexual relationships; but he went too far in this and inadvertently made dwarves biologically non-viable. 

He describes the 'slow increase' in their numbers; but from the information given dwarf numbers could not increase at all over the long term, but would inevitably decline - since dwarf fertility was far below the minimum rate needed to replace those who died. 

The fact that dwarf women were only about 1/3 of the population means that each woman would need to replace herself, and two men - plus a margin to account for death before the age of fertility. So minimum replacement fertility would be three-point-something. 

But we are also told that not-all the dwarf-women took husbands (and it is implied they did not reproduce at all) meaning that women were effectively less than 1/3 of the dwarves. 

Therefore each dwarf women who did reproduce would need to have considerably more than three-point-something children. For instance perhaps only 1/4 of the dwarves were women who reproduced - meaning that the minimum replacement level would need to be four-point-something children per dwarf women. 

However, we are told that dwarf-women only rarely had as many as four children; and the tone of the passage suggests that four children was an upper limit and the usual number was considerably less.  

Putting this all together; this means that the dwarves fertility was less than the minimum required to replace those who died.  

There could be a modest increase before the first generation of dwarves began to die out. Their 'average' life expectancy was given as 250 years. However, this number did not take account of premature deaths; and it is described in Tolkien's writings that large numbers of dwarves were slain in battle, through all the ages of the world. 

And Tolkien also says that dwarves married later than 90 years old - so only a couple of new generations could be fitted-in before even the first dwarf generation began to die out (even if only a small proportion of these founders were slain prematurely). 

Pretty obviously this was a mistake of Tolkien's - and he would have wanted to revise it had the problem been pointed-out. 

The simplest solution would be to state that those dwarf women who did have children had enormous families. 

Alternatively, we can imagine a tragic scenario where a large first generation of dwarves was created - but after a couple of hundred years, the race began inexorably to go extinct...