I noticed the Aloha Editor was still listing IE8 as supported at https://aloha-editor.org/supported-browsers.php as of November 2012 (which is the date that was listed on the page when I checked it). However, that doesn’t mean the Front-end Editor plugin supports IE8.
Just to see if I could find any issues, I tested with IE8 on Windows XP and I couldn’t reproduce the problem using the Aloha Editor demo site: https://aloha-editor.org/demos/wordpress-demo/ (just as a basic test, it doesn’t let you save)
Then I tested with the Front-end Editor 2.3 on a WP 3.5.2 blog with IE8 on Windows XP and I found that my revision saved for my test post content before editing on the front end looked like this
This is a test post
link <a href="https://www.google.com/">one</a>
link <a href="https://www.wordpress.com/">two</a>
link <a href="https://yahoo.com/">three</a>
The revision saved for my test post content after editing on the front end looked like this:
<P>one</P>
<P>two</P>
<P>three</P>
<P>This is a test post</P>
<P>link <A href="https://www.google.com/">one</A></P>
<P>link <A href="https://www.wordpress.com/">two</A></P>
<P>link <A href="https://yahoo.com/">three</A></P>
And it looked liked this when I viewed it via Firebug Lite in IE:
<p><P>one</P><br />
<P>two</P><br />
<P>three</P><br />
<P>This is a test post</P><br />
<P>link <A href="https://www.google.com/">one</A></P><br />
<P>link <A href="https://www.wordpress.com/">two</A></P><br />
<P>link <A href="https://yahoo.com/">three</A></P></p>
Google discontinued IE8 support last year: https://googleappsupdates.blogspot.co.uk/2012/09/supporting-modern-browsers-internet.html
I don’t think it’s very likely work will be done to extend support to IE8 for this plugin unless you contracted and paid for that to get done (assuming a developer would be willing to take it on, which they might not).
?? Long story short, I agree with upgrading, or switching to a different browser such as Firefox, if at all possible.