Ran into this as well for a private site where everybody’s on the local network and has the same IP. What seems to work for this setup anyway was an edit to core.php. Instead of having it drop entries from the online list by IP, have it do it by username instead. Starts at line 148 on my copy of the plugin, replaced that section with this.
// Purge table
$wpdb->query( $wpdb->prepare( "
DELETE FROM $wpdb->useronline
WHERE user_name = %s
OR timestamp < DATE_SUB(CURRENT_TIMESTAMP, INTERVAL %d SECOND)
", $user_name, self::$options->timeout ) );
The support guys were apparently unavailable for a bit, but they’re back now.
I originally had this issue as well after I bought the plugin a couple of weeks ago, they didn’t do anything regardless of what browser I was using. An update took care of it, those buttons are working again.