Nerve damage. Spinal cord injuries usually result in nerve injuries. Thus, nerves that travel to or from the bladder may become severed. The bladder muscle needs nerve connection to the spinal cord to maintain tone. Damage to nerves leaving the bladder can lead to loss of bladder sensation. Same applies to the muscles which cotrol the urinary sphincters and hence can affect urinary continence.
See below. The spinal cord at the level of the control of the bladder (or above) results in lose of the spinal signals to the detrusor muscle of the bladder which normally keeps the muscle at high tone to keep the urine from being released until either voluntary signals from the person are sent or the reflex circuit from the spinal cord to bladder is activated by incr pressure. Thus, no signal, no control.