The problem have been mentioned from previous support thread. Here is the solution quoted from the plugin author:
Hello,
Super RSS Reader uses WordPress’s default RSS engine for fetching feeds.
So inorder to refresh feeds, you need to add a filter to WordPress. Add the below code to the function.php file of your theme.
add_filter( ‘wp_feed_cache_transient_lifetime’, create_function(‘$a’, ‘return 1800;’) );
Here 1800 indicates 30 minutes. Change this according to your needs.
Note: Constantly refreshing feed cache will slow down your server and website. So it is a good idea to leave it to the default.
I love the plugin but it only seems to refresh over night so it is a day out of date.