My fire Finch babies died at 13 days old. The parents were very attentive, but young. Why did they die?

The parents were dedicated, but about 3 days ago they stopped sitting on the nest regularly. They still fed the chicks, and the male sang to them. I heard them begging when a parent went into the nest up till today. Tonight I found them both dead in the nest. The female has some missing feathers at the back of the neck and looks smaller than the male. Why would she abandon teh nest and leave the chicks to die. The parents I have had for about 5 months, so they are young. They are not easily disturbed, and don't cheep or flutter when the cage is approached. They were left pretty much alone through the whole nesting process. Should I let them have another clutch?