The airplanes need to be certified for a rapid descent in case of depressurization, and most commercial planes are not rated for that high of an altitude (it is based on the rate of descent)

You also need to fly faster to have enough lift, and it's also more difficult to reach high speeds.

Why don't airliners fly above FL400? Simply because most are not physically capable of doing so. They are designed to fly within a certain performance envelope and altitudes above FL400 are beyond it. The wing design needs to be able to perform up there as well as down low while maneuvering for landing. Getting a wing that can do both and expand that performance envelope to over 40,000ft is something only the latest generation of aircraft (like the Boeing 737 NG models at FL410) have and it's not by much. The 787 Dreamliner & A380 are to have a service ceilings of 43,000 ft which will be the highest of all airliners in service. True, you do use less fuel as you go higher because the air thins but something else to consider is there less air available at those altitudes to create lift and give the engines power. It's a matter of cost VS efficiency. Flying around under FL400 is fine as no airline is going to go out and buy a whole new fleet of aircraft so they can fly high so as to increase fuel savings. With the use of more composites, blended winglets, improved engine and more efficient wings airlines are already seeing increased efficiency so there isn't a drive to go higher. Plus, in the flight levels above 40,000 engine power output drops dramatically and the wing needs an increasing angle of attack, to create more lift to hold the airplane up as the air is so thin. At some point there won't be enough power available to accelerate the airplane and the angle of attack on the wing will continue to increase just to hold altitude. In that situation the airplane isn't able to speed up and an aerodynamic stall of the wing becomes inevitable. The other critical issue with high flight is the effect of Mach. Even though the airplane is flying well under the speed of sound, air accelerating over the wing can come close to, or exceed Mach 1. In that situation a shock wave develops and laminar airflow over the wing is disrupted. This can cause "Mach buffet" which can lead to a nose-down tuck and a loss of control of the aircraft. http://www.grc.nasa.gov/WWW/K-12/airplane/mach.html

As others have put very well, the reasons for not going much above FL400 is to avoid the problem of thin air and engine power, as well as dealing with the effects of coming close to Mach 1 around the airflow over the wing. Most planes reach their maximum fuel effiency at or around 40,000 feet. If you go too much higher you risk what I just stated, if you go too much lower, you would also waste fuel.

Service ceiling of the 767 is 43,100 ft, and the 747-400 is 45,100 ft. The aircraft weight generally doesn't get low enough in flight to make going above 40,000 worthwhile, though occasionally a combination of light weight, and winds can mean that it does happen. At FL430 in the 767, it is very quiet. I've taken a 747-400 to FL450, but it was on an empty ferry flight (weight would have been around 205 tonnes). Any payload and it would be too heavy to go there. And for those that understand...the yellow lines are very close.