Why are Squibs not notified by the Ministry of Magic

Question

In an interview with JK Rowling she answered this question.

... Also how does the Ministry of Magic find out these kids have powers? ... JKR. The Ministry of Magic doesn't find out which children are magic. In Hogwarts there's a magical quill which detects the birth of a magical child, and writes his or her name down in a large parchment book. Every year Professor McGonagall checks the book, and sends owls to the people who are turning 11. (source: Online chat transcript, Scholastic.com, 3 February 2000)

And yet Nevil was unsure if he was a squib or not until his letter arrived.

If the parchment is a list of all magical births, why are squibs either not known, (due to their exclusion from the list) or the information is restricted? It seems the family would want to start making plans for their child as early as possible.

Answer 1

The Pottermore text on the Quill of Acceptance and the Book of Admittance, which we can safely assume are the book and quill referred to in the interview you quoted, contradicts the interview slightly. It states the following:

At the precise moment that a child first exhibits signs of magic, the Quill, which is believed to have been taken from an Augurey, floats up out of its inkpot and attempts to inscribe the name of that child upon the pages of the Book [...] A mere whiff of magic suffices for the Quill. The Book, however, will often snap shut, refusing to be written upon until it receives sufficiently dramatic evidence of magical ability.

The important change here is that a child's name is not written when they are born, but when they exhibit signs of magic. The Pottermore text also explains why:

Non-magic children born to witches and wizards occasionally have some small, residual aura of magic about them due to their parents, but once their parents [sic] magic has worn off them it becomes clear that they will never have the ability to perform spells.

Therefore, according to the Pottermore article, no one can know in advance whether a child will turn out to be a wizard or a Squib, because even the Book and Quill do not. I'm taking the liberty to use Pottermore here since it's usually placed at the same level of canonicity as interviews - it's technically Word of God. But if you do not recognize the canonicity of JKR's Pottermore writing, I'll try to come up with something else. :)

Answer 2

They are notified by not receiving a letter.

Squibs and their families are notified when the Squib child does not receive a letter from Hogwarts. Angus Buchanan’s siblings were concealing from his parents that he was a Squib, so they had to forge him a Hogwarts letter when none actually had arrived to keep their parents from finding out.

The deception was innocently begun, but as the time approached for him to leave for Hogwarts, Angus and his siblings became uneasily aware that they could not maintain the pretence much longer. No letter from school arrived for Angus, but his panicking sister Flora forged one, which kept the parents in ignorance for several weeks more.
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Therefore, usually, Squibs and their families would find out for certain that they are Squibs when they would be due to start Hogwarts but do not receive any Hogwarts letters.