Why Does 'Overflow:Hidden' Prevent 'Position:Sticky' from Working

Position sticky not working with body{ overflow-x: hidden; }

As far as I know, you cannot use it by now.
It is still only partially supported in some browsers.

When you want to know how far it is with this feature, I can advise you to check it on caniuse.com.

Sticky Feature: https://caniuse.com/#feat=css-sticky

Which CSS settings can prevent `position: sticky` from working?

I think I discovered the reason: if an element is contained in another element which has overflow:hidden, then position:sticky is ignored.

See the following snippet, which I adapted from @Daniel's:

.parent {  position: relative;  background: #ccc;  width: 500px;  height: 150px;  overflow: auto;  margin-bottom: 20px;}
.hidden-overflow { overflow: hidden;}
.sticky { position: sticky; background: #333; text-align: center; color: #fff; top: 10px;}
<div class="parent">  <div>    <div class="sticky">      Hi, I am a sticky inside the container which contains the first paragraph.    </div>    <p>      Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus volutpat sed metus et porttitor. Integer bibendum lacus eget massa ultricies fermentum. Donec cursus magna eu congue posuere. Sed eget ligula quam. Sed laoreet enim sapien, eget volutpat nisl pellentesque vel. Nulla id dolor sed dolor sodales tristique. Curabitur feugiat massa sed massa bibendum semper et ac orci. In imperdiet nibh quis iaculis viverra. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Quisque vestibulum, nunc non volutpat tristique, nisl nisi volutpat nibh, quis pulvinar purus ex nec justo. Sed a cursus turpis. Quisque nulla odio, lacinia quis vestibulum sit amet, elementum laoreet nisi. Etiam aliquet ligula sagittis,    consectetur ipsum sit amet, sodales augue.    </p>  </div>  <p>    Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus volutpat sed metus et porttitor. Integer bibendum lacus eget massa ultricies fermentum. Donec cursus magna eu congue posuere. Sed eget ligula quam. Sed laoreet enim sapien, eget volutpat    nisl pellentesque vel. Nulla id dolor sed dolor sodales tristique. Curabitur feugiat massa sed massa bibendum semper et ac orci. In imperdiet nibh quis iaculis viverra. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos    himenaeos. Quisque vestibulum, nunc non volutpat tristique, nisl nisi volutpat nibh, quis pulvinar purus ex nec justo. Sed a cursus turpis. Quisque nulla odio, lacinia quis vestibulum sit amet, elementum laoreet nisi. Etiam aliquet ligula sagittis,    consectetur ipsum sit amet, sodales augue.  </p>  <p>    Integer congue augue a quam tincidunt, vitae dictum sem iaculis. Proin feugiat nibh vitae leo facilisis, eget laoreet augue dictum. Nunc facilisis tempor feugiat. Aenean eget interdum diam. Maecenas non risus iaculis, scelerisque ipsum eu, facilisis urna.    Integer velit justo, vestibulum vel vulputate vel, bibendum eu lorem. Phasellus viverra nisl a mi pretium eleifend.  </p></div><div class="parent">  <div class="hidden-overflow">    <div class="sticky">      Hi, I am another sticky in the container which contains the first paragraph, but my container has overflow:hidden.    </div>    <p>      Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus volutpat sed metus et porttitor. Integer bibendum lacus eget massa ultricies fermentum. Donec cursus magna eu congue posuere. Sed eget ligula quam. Sed laoreet enim sapien, eget volutpat nisl pellentesque vel. Nulla id dolor sed dolor sodales tristique. Curabitur feugiat massa sed massa bibendum semper et ac orci. In imperdiet nibh quis iaculis viverra. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Quisque vestibulum, nunc non volutpat tristique, nisl nisi volutpat nibh, quis pulvinar purus ex nec justo. Sed a cursus turpis. Quisque nulla odio, lacinia quis vestibulum sit amet, elementum laoreet nisi. Etiam aliquet ligula sagittis,    consectetur ipsum sit amet, sodales augue.    </p>  </div>  <p>    Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus volutpat sed metus et porttitor. Integer bibendum lacus eget massa ultricies fermentum. Donec cursus magna eu congue posuere. Sed eget ligula quam. Sed laoreet enim sapien, eget volutpat    nisl pellentesque vel. Nulla id dolor sed dolor sodales tristique. Curabitur feugiat massa sed massa bibendum semper et ac orci. In imperdiet nibh quis iaculis viverra. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos    himenaeos. Quisque vestibulum, nunc non volutpat tristique, nisl nisi volutpat nibh, quis pulvinar purus ex nec justo. Sed a cursus turpis. Quisque nulla odio, lacinia quis vestibulum sit amet, elementum laoreet nisi. Etiam aliquet ligula sagittis,    consectetur ipsum sit amet, sodales augue.  </p>  <p>    Integer congue augue a quam tincidunt, vitae dictum sem iaculis. Proin feugiat nibh vitae leo facilisis, eget laoreet augue dictum. Nunc facilisis tempor feugiat. Aenean eget interdum diam. Maecenas non risus iaculis, scelerisque ipsum eu, facilisis urna.    Integer velit justo, vestibulum vel vulputate vel, bibendum eu lorem. Phasellus viverra nisl a mi pretium eleifend.  </p></div>

How does the position: sticky; property work?

Sticky positioning is a hybrid of relative and fixed positioning. The element is treated as relative positioned until it crosses a specified threshold, at which point it is treated as fixed positioned.

...

You must specify a threshold with at least one of top, right, bottom, or left for sticky positioning to behave as expected. Otherwise, it will be indistinguishable from relative positioning.
[source: MDN]

So in your example, you have to define the position where it should stick in the end by using the top property.

html, body {
height: 200%;
}

nav {
position: sticky;
position: -webkit-sticky;
top: 0; /* required */
}

.nav-selections {
text-transform: uppercase;
letter-spacing: 5px;
font: 18px "lato", sans-serif;
display: inline-block;
text-decoration: none;
color: white;
padding: 18px;
float: right;
margin-left: 50px;
transition: 1.5s;
}

.nav-selections:hover {
transition: 1.5s;
color: black;
}

ul {
background-color: #B79b58;
overflow: auto;
}

li {
list-style-type: none;
}
<nav>
<ul align="left">
<li><a href="#/contact" class="nav-selections" style="margin-right:35px;">Contact</a></li>
<li><a href="#/about" class="nav-selections">About</a></li>
<li><a href="#/products" class="nav-selections">Products</a></li>
<li><a href="#" class="nav-selections">Home</a></li>
</ul>
</nav>

when css position sticky stops sticking

This question: https://stackoverflow.com/a/45530506 answers the problem.

Once the "sticky div" reaches the edge of the screen, it is at the end of the viewport of the parent element. This causes the sticky element to stop and stay at the end of parent's viewport. This code pen provides an example: https://codepen.io/anon/pen/JOOBxg