How then, could Harry's "perfect" invisibility cloak be made?
Initially the reader is left to think that the story of the three brothers was true, and consequently the deathly hallows. However, Hermione did mention that it was probably more likely that the three brothers were powerful wizards and forged the items themselves.
More likely than not, they discovered some sort of powerful magic which has since been lost.
I have no source for what I am telling you. I am just asuming based on information from Potter Wiki, Pottermore and the famous book ''Fantastic beasts and where to find them''.
But as we know, the Peverell brothers were powerful magicians, so there is no doubt that magic is involved. Hermione is mentioning they may have forged the objects themselves.
My guess is that the cloaks who loses their invisibility is mostly made using Disillusionment Charm or a Bedazzlement Hex, whilst the cloak Harry possesses is made out of Demiguise pelt. In FBWFT (Fantastic Beasts and Where to Find Them) it's stated that Demiguise pelt is used for Cloaks, but on the Potter Wiki it is added a sentence which makes me come to my later conclusion: Cloaks made from their hair eventually turn opaque, losing their invisibility effects as time passes.
What if Ignotus was a very skilled hunter, aswell as a tailor? Maybe he managed to weave the hair of a Demiguise in a sertain way and maybe he knew how to treat the pelt so it would never fade?