Unfortunately I do not share your optimism. I think that the ending of this excellent story actually clearly indicates that the birds will triumph in the end. However, if I were of a more optimistic disposition, I would want to focus on the following three elements that give hope to Nat's family.
Firstly, note the following quote:
He had a new scheme for the windows, which was to fix barbed wire in front of the boards.
Nat shows himself to be ingenious and handy at creating defences against the birds, and the fact that he has not lost hope is shown through his continual thinking of how to defend the house and his family.
Secondly, the fact that the birds only attack every six hours and then rest for six hours gives Nat and his family a chance to restock and defend themselves once again, going to get food and provisions. In theory, they could carry on like this endlessly, defending themselves and constructing new defences during the lull in attack.
Lastly, and most importantly, I would refer to the strength of the human spirit as demonstrated by Nat and the way that he is determined to survive and keeps the spirits of his family up, taking care of them.