Right, you lose pixels when you crop (or trim, same thing).
The camera LCD lets you scroll around on the zoomed image, and you can do the same in your photo editor after zooming.
But once you crop (or trim), then all the rest is gone, and you are left with a smaller image (pixel dimension wise).
The answer (to the loss of pixels when zooming) is to zoom with your camera lens, before you snap the shutter. Then you capture that zoomed picture, but still have full pixel resolution.