My Battle with Line Breaks

Can someone clue me in with what the deal is with WP and line breaks… I know I am not going crazy here but, for some reason, whether I add a simple return in visual mode or I go into the html and add a bunch of
tags, the line breaks will not stick after update.

what am I doing wrong here and why is this not sticking? It is something I need to know?

Thanks for any help or advice on this,

Paul