One of my first theories

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The greatest loss come the interaction of the sphere or cuboid with the oil since this kind of interaction is the study of fluid dynamics (Navier-Stokes equation is almost impossible to solve) and for the fact that it is harder to move in water than in air, it is even harder to move in oil than in water. Since oil is much more viscous than water.
 
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I think I've listed all of them...
With regards to the cyclic motion, you're just converting potential energy into kinetic and vice versa. There is no actual loss there, in the sence of unrecoverable loss. The only unrecoverable losses are to heat, in case of non ideal conditions. I've listed the mechanisms for that earlier.

What you have is this:
PE + KE + W + Q = const.
where:
PE = potential energy
KE = kinetic energy
W = work done
Q = heat produced

As you can see, if Q or W are increasing (meaning work and/or heat are being produced), PE+KE must be decreasing. When PE+KE reaches 0, the system will stop.
 

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