I am sorry about the loss of the chicks. Every breeding pair of birds needs to be rested between clutches of chicks. You need to remove the nest and let them rest for a few months. In this case, I would take the nest away and rest them for at least six months. Then try again and if the same thing happens, then it is time to retire this pair. It sounds like they have been over bred, or possibly they are getting too old to breed. They are losing interest in the chicks when they leave the nest and my guess it they are not feeding them at this point and the chicks are starving to death. If you do let this pair breed again after a good rest, and the chicks leave the nest the same way, put some spray millet and water on the cage floor near the chicks and see if they will self feed. You can also offer seeds and cooked eggs.
Thank you for asking Lafeber,