submit button stays hover color after clicked

You are very close to the solution. In order to achieve the effect you are looking for try using focus and active instead of hover and focus.

The active state is only triggered when the element is being clicked.

Here is what I did

.buttons input:focus {
  outline: none
}
.buttons input:active {
  border: 0;
  background-color: #50627E;
  outline: none;
  -webkit-box-shadow: 0 0 1px rgba(0, 0, 0, .75);
  -moz-box-shadow: 0 0 1px rgba(0, 0, 0, .75);
  box-shadow: 0 0 1px rgba(0, 0, 0, .75);
}

You can check the full solution bellow:

.form input:focus {
  background: #FFFFAD;
  outline: none;
}
.buttons {
  text-align: left;
}
.buttons input {
  font-size: 2.5em;
  font-weight: bold;
  font-family: "Arial", serif;
  padding: 8px 40px;
  background: #4470B6;
  border: 0px;
  margin-left: 0px;
  margin-right: 50px;
  margin-top: 50px;
  -moz-border-radius: 50px;
  -webkit-border-radius: 50px;
  border-radius: 50px;
  -webkit-box-shadow: 0 0 4px rgba(0, 0, 0, .75);
  -moz-box-shadow: 0 0 4px rgba(0, 0, 0, .75);
  box-shadow: 0 0 4px rgba(0, 0, 0, .75);
  color: #FFFAFA;
}

.buttons input:focus {
  outline: none
}
.buttons input:active {
  border: 0;
  background-color: #50627E;
  outline: none;
  -webkit-box-shadow: 0 0 1px rgba(0, 0, 0, .75);
  -moz-box-shadow: 0 0 1px rgba(0, 0, 0, .75);
  box-shadow: 0 0 1px rgba(0, 0, 0, .75);
}
<!--  Details Form -->

<section class="details">
  <form id="form" action="test.php" method="post" autocomplete="on" target="_blank">

    <div class="form">
      <label>First Name:</label>
      <input type="text" name="firstname" placeholder="First Name" autofocus />
    </div>

    <div class="buttons">
      <input type="submit" value="Search">
      <input type="reset" value="Reset">
    </div>
  </form>
</section>

i assume you are styling your button on focus in order to get rid of the outline, so simply split the selector into 2 and on focus remove only the outline:

.form input:focus {
  background: #FFFFAD;
  outline: none;
}
.buttons {
  text-align: left;
}
.buttons input {
  font-size: 2.5em;
  font-weight: bold;
  font-family: "Arial", serif;
  padding: 8px 40px;
  background: #4470B6;
  border: 0px;
  margin-left: 0px;
  margin-right: 50px;
  margin-top: 50px;
  -moz-border-radius: 50px;
  -webkit-border-radius: 50px;
  border-radius: 50px;
  -webkit-box-shadow: 0 0 4px rgba(0, 0, 0, .75);
  -moz-box-shadow: 0 0 4px rgba(0, 0, 0, .75);
  box-shadow: 0 0 4px rgba(0, 0, 0, .75);
  color: #FFFAFA;
}
.buttons input:hover
{
  background-color: #50627E;
  outline: none;
  -webkit-box-shadow: 0 0 1px rgba(0, 0, 0, .75);
  -moz-box-shadow: 0 0 1px rgba(0, 0, 0, .75);
  box-shadow: 0 0 1px rgba(0, 0, 0, .75);
}
.buttons input:focus {
  outline: none;
}
<!--  Details Form -->

<section class="details">
  <form id="form" action="test.php" method="post" autocomplete="on" target="_blank">

    <div class="form">
      <label>First Name:</label>
      <input type="text" name="firstname" placeholder="First Name" autofocus />
    </div>

    <div class="buttons">
      <input type="submit" value="Search">
      <input type="reset" value="Reset">
    </div>
  </form>
</section>

Tags:

Html

Css

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