My back air suspension is not working.

First, check to make sure the air pump switch is "on" and nott turned off due to a tire change or other suspension work. Look in your owner manual for the location in the trunk.
Did you just have repair work done?
Also, check fuses & relays. Info in owner manual.
Let us know what you find so we can help.

Basically, this system has rubber air bladders that have lines running from an electric pump that inflates or deflates the air bags (springs). There is a small computer box that reads a height sensor in the rear, It will add air if too low, and let air out if too high.

Is yours fully deflated?

This seems to be a reacuring problem with the 99 Continental. A good Place to go is strutmasters.com They have some greatconversion kits that convert you from the airbag to a powder coated American made steel coil spring that is guaranteed to last the life of the car. Airbags and compressors are constantly having to be replaced. Also something alot of people don't know is that theses air suspensions are not meant to be in temperatures above 90 Degrees or below 40 Degrees. That is most of the world. The temperature will cause you to replace alot of bags. and typically when your replacing a bag you are going to have to replace the compressor to because the bag had a hole or small crack in it causing the compressor to over work and it will die. I posted the link below so you can take a look http://www.strutmasters.com/lincoln-continental-suspension-s/38.htm I hope I was of some help Good Luck!!!