While I definitely feel a stronger and, more importantly, a more interesting excuse could have been thought up, the excuse they went with is understandable. Bron comes back to the mysterious wastes and finds the land destroyed by a cataclysmic earthquake, his wife dead, and his son MIA. By all accounts, he came back and found everything he cared about in ruins. Sure, he could have tracked down the ultimate fate of his son, and he did, in fact, give up on him being alive, but he could have been afraid to track him down and find him dead. I've heard some families who've had missing family members talk about how they feel that finding their loved one's body would destroy a lingering hope in them that their family could still be alive, and the fact that that chance is so astronomically small keeps them from pursuing it.
Judging by his reaction, he seemed certain that Littlefoot was dead, and didn't seem too guilt ridden that he had thought he had died. Given this world where people die all the time and the people of this world seem much more resigned to their mortality than the 'anything you can put your mind to' attitude you see in most works, his reaction seems like something a normal person would have. It's not a heroic or amiable response, but it at least a believable one. I certainly think it could have been done much, much better, but as it stands, I think his excuse is passable.
