I have experience with custom air suspension before, so I'm asking this question based on LR L322 operation.

MY08 HSE (USA)

My air compressor turns on on every cold start and runs for some time (at least 2 min), stops, then runs again - presumably because it's overheating and needs to cool down. Is the system from the compressor to the air tank/reservoir and valves supposed to hold air at all times, or is it supposed to release air somewhere after some time of inoperation as part of some LR system procedure? O do not have any fault codes.

All four of my air bags hold air on all heights overnight (off-road, standard, access). There are absolutely no leaks with measurement being exactly the same from ground to fender.

I am going to spray some soapy water at fittings throughout and wanted to know where common trouble areas are. However, I also wanted to know first if I am approaching this for the wrong reason -of whether depressurizing the air tank is normal operation or not. In the mean time, I've pulled fuse F13 5A for air suspension in the rear fuse box to prevent possible compressor overuse with the expected ding, fault message normal height only, and a disabled terrain response + height adjust switch (no illumination). Thanks in advance for responding.

As far as I know the system only releases air to lower the car when requested, or to keep the car level when there is a leak on one corner (When parked overnight for instance )
Sounds like most of your system is ok, but if the compressor is running overtime you could have a small leak between the compressor and air cylinder or from the air cylinder, definitely worth the soapy water test.

Also your compressor could have lost some efficiency and need an overhaul ( Overhaul kits are cheap and an overhaul is not a big job ) Hope this helps

PS - Noticed this is your first post - Check out the Wiki section for info, and a search of previous posts will reveal a wealth of invaluable info from the members on here.

Remember your compressor is 15yrs old and this wouldn't surprise me being the problem if you've checked heights over time...