You are using the shorthand border-image property for setting the size of the gradient and according to the values provided, the top, left and right borders are nullified.

Setting 100% as width of the border gradient on top and 3px as its height would result in the gradient getting applied only on top and bottom.

border-image: linear-gradient(to left, rgba(0, 0, 0, 1) 1%, rgba(0, 255, 255, 1) 50%, rgba(0, 0, 0, 1) 100%) 
              100% 0 100% 0/3px 0 3px 0 stretch;

In the above lines of code, the 100% 0 100% 0/3px 0 3px 0 represents the size of the gradient border on each side (read as [top] [right] [bottom] [left]). Originally it was 0 0 100% 0/0 0 3px 0.

div {
  /* gradient shining border */
  border-style: solid;
  border-width: 3px;
  border-image: linear-gradient(to left, rgba(0, 0, 0, 1) 1%, rgba(0, 255, 255, 1) 50%, rgba(0, 0, 0, 1) 100%) 
                100% 0 100% 0/3px 0 3px 0 stretch;
  
  /* other demo stuff */
  height: 50px;
  line-height: 50px;
  background-color: #222;
  color: white;
  text-align: center;  
}

<div>Some content</div>

Note that border-image property still has pretty low browser support and would not work if you need to support IE10 and lower. Instead of it, you could use background-image like in the below snippet to produce a similar effect though. This works in IE10 also (but still wouldn't work in IE9- because they do not support gradients at all).

div {
  /* gradient shining border */
  background-image: linear-gradient(to left, rgba(0, 0, 0, 1) 1%, rgba(0, 255, 255, 1) 50%, rgba(0, 0, 0, 1) 100%), 
                    linear-gradient(to left, rgba(0, 0, 0, 1) 1%, rgba(0, 255, 255, 1) 50%, rgba(0, 0, 0, 1) 100%);
  background-size: 100% 3px;
  background-position: 0% 0%, 0% 100%;
  background-repeat: no-repeat;
  
  /* other demo stuff */
  height: 50px;
  line-height: 50px;
  background-color: #222;
  color: white;
  text-align: center;
}

<div>Some content</div>