Many owners mistakenly believe that an engine should only be overhauled for hours. Let it sit for 30 years and it flies ten hours off of a 1,600 hour TBO...it still ought to have 1,590 hours until recommended overhaul, right?
Wrong. It should be overhauled immediately, if not scrapped. Sitting is death on engines and airplanes. As USMCMech said, it's the worst possible thing you can do short of setting the airplane on fire.
If the airplane didn't fly for 31 years, then it shouldn't have flown until being overhauled right off the bat.
Don't get caught up in compression readings meaning much of anything. Compression tests are generally meaningful to those who don't know better, and salesmen. Otherwise, unless every test was performed at the same temperature, using the same mechanic, using the same compressor and test set...too many variables exist to make the reading anything but significant by passing interest only.
Each time you do a compression test, the compression may go up or down, and that doesn't really mean a thing. Finding out why it did might...but don't assume that an engine with high compression is a good engine, any more than one that doesn't test well is a bad engine. It's just not the case.
Think in terms of age and time as well as hours. An engine that doesn't fly for three or four months should still undergo an oil change; acids are still washing into the oil, the oil can still be contaminated, and damage can still occur. An engine should be run regularly. You should be doing regular spectrometric oil analysis with every oil change, and the less you fly, the more you should consider changing the oil. Sitting idle kills mechanical things, especially airplane things.
Getting back to my previous question...where is the oil going? Blowing out the breather? Are you finding it on the belly? When uncowling the engine, is it wet? Are you finding fouled spark plugs to be a problem? Dark brown deposits showing up inside the lips of your exhaust stacks? You keep putting it in the engine, but you need to find out where it's going. For every bit the reason that you wouldn't do brain surgery merely because someone has a headache, looking at a teardown merely because you are losing some oil may be a bit premature. Let's find out where that oil is going, first.