The EAS on both the Range Rover and Discovery of your vintage are notorious for having problems and they are never inexpensive to repair. That is why most people convert them to regular coil springs. One of the big problems with the EAS is the original air springs which tend to leak when they get older and especially in cold weather. Many people don't replace their air springs when this happens and of course the air compressor runs more frequently and air valves/solenoids are constantly opening and closing thus dramatically shortening their life. The dealer is really the only place to go to diagnose your problem properly as they'll hook up your car to their autologic computer and it'll help to tell them what's up. All the components of the EAS are expensive so you don't want to be using the diagnosis by parts replacement method and even if you were to do it that way, you would still need the dealer to recalibrate the EAS if any height sensors were replaced.
Now as to your particular problem, unless you have a massive leak in your air springs, they should inflate immediatly and quickly upon engine start-up. Sounds to me like you probably need new air springs for starters but you may also have a bad compressor, faulty valve block, leaky lines, leaky air tank or a combination of all.
Regarding your question whether it is ok sitting sunk in the back, it's ok but you may get an EAS malfunction warning when you start the truck. This has happened to me on my Range Rover, but after the suspension pumped up and I shut off the ignition and then restarted it, the malfunction warning disappeared. Not sure if your Disco will behave the same way. If the warning remains, you're off to the dealer for a reset. Regarding you're other question, it is ok to drive with the vehicle sunk down or even on the bump stops, but only at very low speed and really only to limp home or to the dealer.
If you do decide to go for new air springs, get the generation II or III from Arnott's. They are vastly superior to OEM and have a lifetime warranty.
Good luck. EAS is nice WHEN IT WORKS. Kinda like Land Rovers in general.
