Hello and thank you for trusting Just Answer with your question. I'm Dj and I will work with you on this.
If you have a leak, you will find the vehicle sitting on the ground when you get up in the morning. It doesn't sound like you have a leak.
If you have a bad compressor, the pump will take a long time to get the vehicle up to level. It doesn't sound like you have a bad compressor.
It sounds like you have a bad height sensor. The controller and the compressor are responding to false signals. When it thinks the vehicle is low, it jacks it up, way up. When it thinks it's too high, it releases pressure and drops the vehicle to the ground. Looks cool, but it's not practical.
If you Google Image "Land Rover Height Sensor" you will see pictures of the sensor. This is a pretty easy diagnosis and fix. You can disconnect the lever and move it up and down and see what the computer does. But it's a fairly safe bet this is just a sensor problem. It's common.
Please let me know if you have any questions.
DJ, Thanks so much for your response! I do have another question... Just this morning for the first time something new happened. At about 6am the truck's alarm starting going off. I turned it off and thought nothing of it. Then at about 8am it happened again. I am now worried that maybe it is a computer problem? What do you think about this?
Here is a web site with a good picture of the sensor. There are two bolts that hold the sensor, and one that holds the lever.
It's likely that just one sensor is failing. But with one jacked up, it will pull the other side up also, but not as far.
So with the car parked on level ground, measure the distance from top of the wheel well to the ground. The highest one is the side with the faulty sensor.
This is about a half hour replacement. The toughest part is getting under the car to get access.