You will find a few threads on here that talk about suspension airbag leaks. Yours is probably a small leak. When using the car, the suspension air compressor keeps the height up. When you park for a while, the air slowly leaks out and the compressor is not on to keep the pressure up, so the car will sink as the air bag loses air.
I mentioned on another post that I had the exact same problem with my 94k 2011 Equus. I bought replacement rear air bags off ebay for $385 delivered and spent $140 to have my indy install them. Problem solved.
I wasn't able to find much about this issue searching through the forums so I figured I'd make a post to help out people who have this issue with their Equus in the future.
I recently purchased a 2012 Hyundai Equus with 46k miles and it was very cheap due to an issue with the brakes. The...