Why is 51,000 ft a common service ceiling for business jets?
If for no other reason, its likely because there is a practical maximum descent speed for a given airframe and aircraft must be able to descend from their maximum cruising altitude to 10,000 ft. in 10 minutes or less. Although under part 135 (how many of these planes are likely flown) the regulations have a few variations you can have less oxygen on board if you can descend in 4 minutes. 

At 51,000 ft. you would need to lose 41,000 ft in 10 minutes or even 4 minutes. That is a descent rate of either 4100 ft/min or a blistering 10,250 ft/min which likely yields a speed at or near Vne for most of these airframes. 

This Gulfstream pilot discusses a bit of it from a practical standpoint here.