max-width not working for table-cell

I guess the reason is quite clear to you now, so i am just going to suggest you a workaround to this. By using display:block/inline-block; instead of display:table/table-cell;.

So the solution is:

div.container {
  width: 100%;
  display: block; /* Changed from display:table; */
}
div.container > * {
  display: inline-block; /* Changed from display:table-cell; */
  float:left; /* Added floating to avoid space between elements */
}
div.middle {
  width: 100%; 
  max-width: 500px;
  background-color: black;
}
div.side {
  width: auto;
  background-color: chocolate;
}

<div class="container">
  <div class="side">Left</div>
  <div class="middle">.</div>
  <div class="side">Right</div>
</div>

Working : Fiddle

Updated Solution:

Found a solution

Going back to tables would work by giving table-layout:fixed; to container.

Working Demo

HTML

<div class="container">
  <div class="side">Left</div>
  <div class="middle">.</div>
  <div class="side">Right</div>
</div>

CSS

html, body {
    width:100%;
    height:100%;
    margin:0;
    padding:0;
}
.container {
    display:table;
    width:100%;
    height:10px;
    table-layout:fixed;
}
.side, .middle {
    display:table-cell;
    text-align:center;
    vertical-align:middle;
}
.middle {
    width:500px;
    background:black;
}
.side {
    width : calc(50% - 500px);
    overflow:hidden;
    background:chocolate;
}

@media (max-width: 500px) {
    .side
    {
        display:none;
    }
    .middle
    {
        width:100%;
    }
}

Thanks Aziz, now I know that max-width shouldn't be used for table cells as

In CSS 2.1, the effect of 'min-width' and 'max-width' on tables, inline tables, table cells, table columns, and column groups is undefined.

Waiting for workarounds...