Responses
Actually it's more like the dragons can only sense the last trace of their mates, not exactly the mate (in this case Solath). However, Eyra was sent to Labyrinth from a really young age. Labyrinth had some kind of stealth magic, so the last trace of Eyra was still in Solath. Yanu knew the fact that Eyra was a Labyrinth mage (which was located to the South), so at first he couldn't figure it out.
(I read this from a spoiler so I'm not so sure myself)
How come Yanu can't tell who his mate is? He just knows they are born in Solath but for a Dragon they should have been able to sense their mate?! I am absolutely sure that they put a spell on Eyra after his birth when they found out he was Yanu's mate.