Let's begin by positing that Force sensitivity is determined by your genes, just like hair color - hey, it's less outlandish a concept than magic blood monsters. We know that Vader, Luke, and Leia are all Force sensitive, and the ability to pass on a trait to offspring is explained through genetics. Barring some astronomical coincidence or metaphysical hokum, it's safe to assume that Vader's Force aptitudes were passed down to his offspring genetically.
But how, exactly, would Force sensitivity be passed down? Would any offspring of a Force user be Force sensitive? Let's look at the genetics.
Half of your genetic material is provided by your father, while the other half comes from your mother. Let's quickly clarify some jargon: genes are found within DNA, and DNA is found within chromosomes.
Different species have different numbers of chromosomes, but what's important is that chromosomes come in pairs - one set of chromosomes inherited from the father, and a matching set inherited from the mother. Every gene on one chromosome has a corresponding gene that it gets matched with on the second chromosome - but those genes are not necessarily identical. Different forms of the same gene are called alleles, and it is how these alleles get paired up that will determine certain traits, such as hair color.
An allele can either be described as dominant or recessive. For a given gene, an individual will either have a pair of dominant alleles, a pair of recessive alleles, or one dominant and one recessive allele. In the case of a pairing of one dominant and one recessive allele, it is the dominant one that determines the trait - thus the name "dominant."
A trait that is determined by a single gene (that is to say, a pairing of alleles of a single gene) is called a Mandalorian Trait - err, a Mendelian Trait. Let's say that Force sensitivity is a Mendelian Trait. What would the genetic makeup of a Force user look like?
Well, we want Force users to be rare, so let's say that the recessive allele is the one that makes someone sensitive to the Force. That would mean a Force user, such as Darth Vader, must have two recessive Force sensitivity alleles. If he had one dominant one and one recessive one, then the dominant one would win out, Vader would have had no Force powers, and Star Wars would have been a much less interesting trilogy.
How about the children?
We know that Luke and Leia are Force sensitive, so they, too, must have two recessive Force sensitivity alleles. But we know that they only received one allele from their father, while the other came from their mother - who was not a Force user. That means that the mother must have had one dominant and one recessive allele - if she had two recessive alleles, she would have been Force sensitive, and if she had two dominant alleles, then it would be impossible for her offspring to be Force sensitive, because she could pass on nothing but a dominant allele.