Exported JPG selection from INDD loses part of the jpg image

First: Why are you making JPGs? 

The PDF looks fine because your elements are still vector.

fyi: Your attached JPG shows all the lines (and are not anti-aliased), but depending on the resolution of the monitor and zoom %, these skinny (literally 1 pixel width) can possibly disappear as they are far thinner than the coarse pixels of your monitor (typically 96ppi).

In any case, as your rules lines are very thin, the chance they will render properly in a rendered image at 300ppi is iffy at best. 1 pixel at 300ppi is the equivalent of 0.24 pt. so if you have a stroke width less than that, say 0.15 pt, you can't render lower than that 0.24pt (with the next step up being 2 pixels = 0.48pt.), and whether you get 1 pixel or two depends on where the stroke falls on the pixel grid You will never get better than what you've attached here at that size.

Turning ON anti-aliasing will it will only make it worse, because any stroke that doesn't fall EXACTLY on a pixel row will be antialiased over two-pixels, with greay values based on how much of the stroke on either side of the boundary. making it blurrier, and each line may have different antiasing depending on how it hits the grid.

The attached shows how thin lines can be antialiased (right) as opposed to not (left). As I said, if the stroke falls between two pixels, each row is rendered a tint of the solid colour. Even if your stroke falls exactly inside a pixel boundary, the result is a dark tint instead of solid colour.