BuddyPress.org

It’s highly unlikely that it’s a bug in the activity stream – hundreds / thousands of sites run the BuddyPress activity stream without problem.

It’s almost certainly something wrong in your bespoke theme / bp-custom.php file.

Have you changed the theme since the second person carried out their activity? Does it show in the main site activity stream? Have you installed some privacy plugins, or has the member specified that their activity is private? Is the site hidden from search engines?

It’s impossible to provide much more help without a lot more information about your site configuration and the details of your theme code.