Great Tits - brood dies

We have a nest box with a camera and, as in previous years, a pair of great tits nested.  They laid 9 eggs, of which 8 hatched.  One chick died the next day, the other 7 survived for about 3 days, then died one by one over the next 5 days.  I noticed that the parents, who were feeding very regularly, were often bringing large flies - perhaps hawthorn flies - and I wonder if that was the only food they could find.  In the nights after the chicks hatched, we had frosts so perhaps there was simply insufficient food.

Has anyone had a similar experience, or any ideas on what may have gone wrong?