I apologize for the inconvenience. The error is in the following line of code:

```html
document.getElementById("task-list").appendChild(liElement);
```

This line of code adds the new task to the end of the task-list ul element. However, the page refreshes before the new task can be added. To fix this, we need to use the insertBefore() method instead of the appendChild() method. The insertBefore() method inserts the new task before the specified element. In this case, we want to insert the new task before the first element in the task-list ul element. So, the code should be changed to the following:

document.getElementById("task-list").insertBefore(liElement, document.getElementById("task-list").firstChild);

This code will insert the new task before the first element in the task-list ul element. Once this change is made, the page will no longer refresh when you add a task.

Here is the updated code:

```html
<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>To-Do List</title>
  <style>
    * {
      font-size: 1em;
      color: #000;
      font-family: Arial;
    }
    body {
      background-color: #ccc;
    }
    DIV.container {
      background-color: #fff;
      margin: auto;
      width: 25%;
      border: 3px solid black;
      padding: 10px;
    }
    .completed {
      text-decoration: line-through;
    }
  </style>
</head>
<body>
  <div class="container">
    <h1>To-Do List</h1>
    <form action="#">
      <input type="text" class="form-control" placeholder="Add new task...">
      <button id="add-task-button" type="submit">Add Task</button>
    </form>
    <ul id="task-list" class="list-group">
      <!-- The tasks will be inserted here -->
    </ul>
  </div>
  <script>
    var addTaskButton = document.getElementById("add-task-button");
    addTaskButton.addEventListener("click", function() {
      var inputValue = document.getElementsByClassName("form-control")[0].value;
      if (inputValue !== "") {
        var liElement = document.createElement("li");
        liElement.innerHTML = inputValue;
        document.getElementById("task-list").insertBefore(liElement, document.getElementById("task-list").firstChild);
        document.getElementsByClassName("form-control")[0].value = "";
      }
    });
    
    // Mark task as completed
    var taskList = document.getElementById("task-list");
    taskList.addEventListener("click", function(event) {
      if (event.target.tagName === "LI") {
        event.target.classList.toggle("completed");
      }
    });
  </script>
</body>
</html>
```

I hope this is helpful!
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