I was going through some posts a few days back and I noticed something unusual; all the dates on the comment were the same as that of the post date. The first culprit that you think of when you see such kind of error is a plugin. Any plugin with compatibility issue or error in coding could have caused the problem... or so, I thought. But then I realised I had just changed my theme. So, it must be an issue with the theme's coding rather than a problem with a plugin.
How To Fix It?
Head over to the Appearance tab on your WordPress interface and select Editor.
Select your current theme from the drop down list at the top.
Now, the code you need to fix might be on any of the two pages : comments.php or functions.php.
Click on comments.php on the list of files under Templates and search for date and time.
If you don't find anything there, look for it on functions.php.
The code responsible for displaying the comment date on my theme has been highlighted below.
Note that the coding for displaying comment date will not always be within the <time> tag, it might be mentioned as <date> or, <comm-date> or anything else.
Now, what you need to do is, replace the content in between the <time> tag. (As I have said above, in your case, it might be <date> or <comm-date> or anything else.)
Put this in between the two tags :
<?php comment_date(); ?>
So, the code highlighted on the image will look like this at the end :
<p><time><?php comment_date(); ?></time></p>