At various times, usually at start up, but frequently while driving, what was diagnosed as a bad air suspension compressor, starts making noise like it is pumping up with bad valve. Air suspenion compressor was replaced, but problems continues. Any advice is appreciated..

 

Is that all that was replaced was the compressor? Usually it is good to look at the air springs as well as the solenoid.

 

Ouch! Was that at a Dealer or an Independent shop? If it was a Dealer, they need to be spanked thoroughly. If it was an Independent, cut them a little slack. Air Suspension is a mystery to many shops.
Whoever did the diag may not have been familiar with Air Suspension. Most often the first problem spots are at the air springs, as y2kfordparts mentioned. The rubber air springs are the wear items in the system. They get stiff, weather checked, and the rubber breaks down over time very much like tires. When they crack and start to leak, the compressor will run to keep up with the leaks. The springs are good for about 10 years, give or take. The rubber pump mounts wear out too, causing the pump to sound louder.

What do you mean by "starts making noise like it is pumping up with bad valve"? Can you elaborate on that? How long had you been having the problem? Have you noticed the back end dropping when parked for more than an hour? This is important to know because you "might" be able to take issue with the shop on the compressor replacement. It was either a bad diagnosis, OR they may have only fixed the symptom and not the cause.
It is possible that the compressor was ok, unless the concern you noticed had been happening for a while and you put off the repair. If the compressor is trying to "keep up" with a leak it won't last long at all. They arent designed to do that.

Have the shop (or a different one) look for cracks in the rear air springs, near the bottom of the "bladder" with the rear axle hanging free. If there are cracks, the springs need to be replaced. That's where they leak. That will be the "cause" for the pump running too often and wearing out. If it actually was worn out depends on how long the springs were leaking.
Other leaks "can" happen but are very uncommon. Leaks at solenoids or line fittings "usually" only happen if parts are replaced without replacing the associated o-rings, or not cleaning the seal areas properly.