I think your problem is here:
$like_the_post = intval( $_POST['like_the_post'] );
You’re relying on the user’s browser’s POST input to determine whether to increment or decrement the count. When a user quickly clicks the button, the AJAX call hasn’t yet completed and changed the form input from true to false (or whatever’s vice-versa). Additionally, this approach is liable to being spammed by a script repeatedly hitting your AJAX script with this value set to ‘true’ to artificially inflate the ‘likes’ on a post.
Since it looks like you’re tracking the user_id when someone clicks the button, I’d suggest changing your AJAX code so that you first check to see if the user already has a record for that post_id – if not, increment the counter, if so decrement.