BuddyPress.org

For anyone else with this issue, here is the fix. Thanks to @sbrajesh

in bp-messages-templatetags.php, starting at line 498:

function bp_send_private_message_link() {
echo bp_get_send_private_message_link();
}
function bp_get_send_private_message_link() {
global $bp;

if ( bp_is_my_profile() || !is_user_logged_in() )
return false;

$user=new WP_User($bp->displayed_user->user_id);

return apply_filters( ‘bp_get_send_private_message_link’, $bp->loggedin_user->domain . $bp->messages->slug . ‘/compose/?r=’ .$bp->displayed_user->userdata->user_login );
}

Private messaging now works with persistent caching like memcached.