[avian]

> If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?

Yes, they do. But it's only a very very tiny amount.

You're shaking both the positive (nucleus) and negative (electrons) parts of the atoms. The electromagnetic fields outside of the atom almost perfectly cancel out. This means that the acceleration only affects the very small residual field and there is very little radiation at far distances, unless you shake it really really fast.

Another way to look at it is that atoms are in fact already constantly shaking by themselves because of thermal movement. And this does in fact result in them emitting radiation: objects at room temperature will radiate in the infrared spectrum because of this.

The trick is that thermal movements of atoms are very fast compared to moving something by hand. Room temperature infrared radiation frequencies are on the order of tens of terahertz. Compare this to manually shaking an object at (say) 10 times a second. With some hand waving math this is like giving it an equivalent temperature of around 10^-10 kelvin. It will radiate extremely long wave radio waves, but such a tiny amount that it will be completely unmeasurable.