In terms of diagnostics, it sounds like the strut has a leak and it's only become noticeable having sat so long. Basic check would be to start the car and let it sort itself out first. Then change the setting to Lift and then spray some mild soapy water on the problematic strut, and check for leaks. If no leak found, another option would be to spray the valve block which is located in the passenger side wheel arch, behind the liner.
If you find the leak, it would also be a good idea to use VCDS and check the output from the compressor (something like 15-16 bar), as depending on how big the leak is and how long it's been there, it can cause excess wear on the compressor. Check the compressor for fault codes, with one for 'cutoff for excess temperature' (not the exact text) being a sign for an overworked compressor. There are repair kits available on eBay.
For more detailed info on their operation, check out the following PDF from the D3 Tech Dump thread starting from page 24:
65-SSP 994303Audi Adaptive Air Suspension.pdf
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2001 A8 D2 FL 3.7 Q - LPG Conversion, Engine: AKC, Gearbox:FBB, Colour:LY5X Aqua Blue pearl effect, Interior:WJ light beige/dark beige valcona leather with burr walnut inserts
My DIY jobs -
Replaced alarm horn,
Replaced Coolant Temp sensor,
Updated RNS-D firmware,
Installed Reversing Camera and Digital TV,
Dashcam Installation,
Retrofitted Rear Blinds,
Auto-Dimming Rear View Mirror,
Chrome Boot Struts
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2008 S8 D3 5.2 V10 - Engine: BSM, Gearbox:KLW, Colour:LY7F Suzuka Grey Pearl Effect, Interior:Black/Black with Silver/Black valcona leather with carbon atlas inserts, Bang & Olufsen, Heated windscreen, Soft-close doors, TV, DAB, AMI, Quad Zone, Auto Boot, Auto dim Mirrors, Keyless entry, PDC with rearview camera, AFS II Headlights
My DIY jobs -
Fan Jet Windscreen Washers,
Retrofitted Electric Side Blinds