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When you compress a bicycle pump and seal the opening, the pump will automatically return to it's initial position when you release it. I suppose this is how air suspension works as well?

enter image description here

if you have a internal combustion engine without any gas and turn it over - for instance with a kickstarter, until the piston reaches the very top on the compression cycle - why doesn't it return to the bottom by itself by the air compression alone? Is there anything blocking this, or is the air simply not powerful enough to turn the engine over?

See comments from Physics StackExchange

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    $\begingroup$ On many pull-start engines, if you stop pulling on the rope at the right moment (just before TDC), you can feel the piston rebounding from the air pressure. It doesn't usually return all the way to BDC, but it definitely moves enough that you can see/feel it in the rope. $\endgroup$ – Carlton Nov 23 '15 at 18:45
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In theory, it should perform as you say. This is how prop starting an aircraft engine works.

An internal combustion engine, unlike your bike pump, is designed for high speed, high power, and high temperatures. These design considerations give it higher internal friction and leakage (valves and cylinder seals) when doing a slow and cold propping operation. This would be a reason why some engines may not respond as expected.

http://www.pipercubforum.com/handprop.htm

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There is another reason for this in multi-cylinder engines. While one cylinder is compressing the air, another is decompressing it. The net result is that the torque as a function of position gets smoother as the number of cylinders is increased.

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