It isn't spelled out exactly what happens to Mafatu at the end of Call it Courage. All we know for sure are two things: First of all, that he faints into the arms of his father, Tavana Nui, after he returns home from his epic voyage. And second, that years after the voyage, the people of Hikeuru still sing Mafatu's story in their chants and tell it around fires. This indicates that Mafatu has entered into mythology as a brave and noble warrior, which is exactly what he'd hoped to do by setting out on his remarkable journey.
In Mafatu's culture, it is common to celebrate the bravery of warriors, to sing of their great deeds and their heroism. And Mafatu, thanks to his exploits, has now joined the pantheon of greats. But as such songs are sung about those who died while performing their heroic deeds and those who lived to fight another day, it simply isn't possible to infer from the last lines of the story what fate befell Mafatu after he collapsed exhausted into his father's arms.
On the whole, it's more than likely that Mafatu survives. He collapses, not because he's about to die but because he's emotionally and physically drained by his epic voyage, as anyone would be in his position. He must also be feeling quite overwhelmed at the welcoming sight of his father, whom he hasn't seen for ages.
Seeing his father again must be a very emotional experience for the brave young man, not to say a source of considerable delight. Mafatu knows that he's made his father proud, and the feeling of joy he must feel because of this, added to his immense physical and mental exhaustion, would be enough to make anyone faint.