The sudden nature of this problem would suggest that it has been caused by a sudden event, which has resulted in a loss of control of the back legs. One common cause, in this case, could be due to a disc disease of the spine. A slipped disc in a dog could put pressure on the nerves in the spinal cord, leading to an interruption of the messages from the brain to the legs. This would result in the dog being unable to coordinate its legs and can in some cases, if left untreated, result in paralysis.
An X-ray may not show up these slipped discs, and so if this is presumed to be the case, a dye will be injected into the spinal column and this should hopefully show up the problem more clearly.
Also, it is important to consider the breed of dog, as some dogs are prone to certain diseases which could be the cause of this problem. Alsatians are one example of this; this is caused by interbreeding.