How to avoid Chrome hide background image and color over an autofill input

You CAN NOT Override the autocomplete code, since it's being controlled by user agent stylesheet, take a look at cascading-order to know more.

Here is the code (i've copied from google chrome) that is making your icons disappear on autocomplete, just in case you were wondering:

input:-internal-autofill-selected {
      background-color: rgb(232, 240, 254) !important;
      background-image: none !important;
      color: -internal-light-dark-color(black, white) !important;
    }

So what now? If you are intent on solving icons disappearing problem here is a hack that you can do it for you:

.form-section .form-control {
  border-radius: 4px;
  background-color: #f7f8fa;
  border: none;
  padding-left: 62px;
  height: 51px;
  font-size: 16px;
  background-repeat: no-repeat;
  background-position: left 17px center;
}

.form-section .form-control:focus {
  -webkit-box-shadow: none;
  box-shadow: none;
}

.form-section .form-group {
  margin-bottom: 21px;
  position: relative;
}

.form-icon {
  position: absolute;
  left: 16px;
  top: 50%;
  transform: translateY(-50%);
}

.form-section .form-control[type="password"] {
  background-image: url('https://i.stack.imgur.com/910l0.png');
}

.form-btn {
  padding: 10px;
  background-color: #65a3fe;
  border: none;
  color: #ffffff;
  font-size: 18px;
  font-weight: 700;
}
<div class="form-section">
<form>
  <div class="form-group">
    <input title="Email" type="email" class="form-control" name="email" placeholder="Your email address" value="">

    <img class="form-icon" src="https://i.stack.imgur.com/xhx3w.png" alt="">
  </div>
  <div class="form-group">
    <input title="Password" type="password" class="form-control" name="password" placeholder="Your Password">
  </div>
  <button type="submit" class="btn btn-primary form-btn">Log in</button>
</form>
</div>

Here you can use any color e.g. white, #DDD, rgba(102, 163, 177, 0.45).

For Background: transparent won't work here so please use colors.

/* Change the white to any color ;) */
input:-webkit-autofill,
input:-webkit-autofill:hover, 
input:-webkit-autofill:focus, 
input:-webkit-autofill:active  {
    -webkit-box-shadow: 0 0 0 30px white inset !important;
}

for text color:

/*Change text in autofill textbox*/
input:-webkit-autofill {
    -webkit-text-fill-color: yellow !important;
}

Your Solution:(for above case)

Use separate div for icon and for input

.form-section .form-control {
	
	font-size: 16px;
  width: 100%;
  margin-left: 9px;
}

.form-section .form-control:focus {
	-webkit-box-shadow: none;
	box-shadow: none;
}

.form-section .form-group {
	margin-bottom: 21px;
}

.icon-email {
	background-image: url('https://i.stack.imgur.com/xhx3w.png');
  background-repeat: no-repeat;
    background-position: center center;
    width: 30px;
    height: auto;
}

.icon-pass {
	background-image: url('https://i.stack.imgur.com/910l0.png');
  background-repeat: no-repeat;
    background-position: center center;
    width: 30px;
    height: auto;
}

.form-btn {
  padding:10px;
    background-color: #65a3fe;
    border: none;
    color: #ffffff;    
    font-size: 18px;
    font-weight: 700;
}

.input-txt{
    padding-left: 5px;
    float:left;
    border-left:none;
    outline:none ;
    border: none;
    background-color: #f7f8fa;
}

.custom-input {
    display: flex; 
    border-radius: 4px;
	background-color: #f7f8fa !important;
	border: none;
	height: 51px;
}
input:-webkit-autofill,
input:-webkit-autofill:hover, 
input:-webkit-autofill:focus, 
input:-webkit-autofill:active  {
    -webkit-box-shadow: 0 0 0 30px #f7f8fa inset !important;
}
<div class="form-section">
    <form>                                 
        <div class="form-group custom-input">
        <div class='icon-email'></div>
            <input title="Email" type="email" class="form-control input-txt" name="email" placeholder="Your email address" value="">
		</div>
        <div class="form-group  custom-input">
        <div class='icon-pass'></div>
            <input title="Password" type="password" class="form-control input-txt" name="password" placeholder="Your Password">
		</div>
        <button type="submit" class="btn btn-primary form-btn">Log in</button>
    </form>
</div>