I tried to catch AJAX requests with Firebug, but there were only search requests. I thought that after selecting there will be also AJAX database updating request, but there was not. But maybe it works other way...
Yes, the connections are stored when you save the post.
So, there's a problem with the table creation.
Please try to run these following two queries in phpMyAdmin and tell me if you get any errors:
CREATE TABLE wp_p2p (
p2p_id bigint(20) unsigned NOT NULL auto_increment,
p2p_from bigint(20) unsigned NOT NULL,
p2p_to bigint(20) unsigned NOT NULL,
PRIMARY KEY (p2p_id),
KEY p2p_from (p2p_from),
KEY p2p_to (p2p_to)
CREATE TABLE wp_p2pmeta (
meta_id bigint(20) unsigned NOT NULL auto_increment,
p2p_id bigint(20) unsigned NOT NULL default '0',
meta_key varchar(255) default NULL,
PRIMARY KEY (meta_id),
KEY p2p_id (p2p_id),
KEY meta_key (meta_key)