I have the same problem with mine. The fig tree carries it's fruits in July but already developes them in autumn. So they overwinter at the branch. Due to the local climate it is possible that some branches just freeze off. When the whole branch is busted the tree develops new shoots in spring. The fruits at these new branches only show in summer. But then it is usually too late to ripen.
Because of this, it is worth to take care of the tree and branches during winter. The toughest time is late winter around January when the sun starts to shine and the night frost hits hard. So I am going to wrap my fig tree in card web this year to obviate the problem and I am going to hope that the fruits will last and not be damaged by late frosts.
The luxury solution would be a florino in combination with a frost protection ;)