The fact that they all disappear at once does indeed suggest a predation, if it was lack of food/disease etc. they would most likely go at different times and the parents either remove them one by one or leave them in the box. Weasels and other small mammals such as mice will readily enter nestboxes and take the clutch.
As for stopping it, I suppose you could put up some sort of barrier on the wall to stop whatever it is climbing up into the box. I'm afraid I'm of the opinion that the predators need to eat too

and many young birds every year never make it out of the nest, but I can understand that it's not very nice when it's 'your' nest, so I would give the barrier thing some thought and see if you could rig something up