The function of search is: from left to right, calculate whether there is a match, and if there is a match, return it. That is, as long as a match is found, it is returned. Therefore, at most one will be matched, not multiple.
findall can match all.

#!/usr/bin/python
# -*- coding: utf-8 -*- 

import re

str = 'xiaohong loves xiaoming,xiaozhu loves xiaoli,xiaopeng loves xiaozhao'

names = re.findall(r'(\S+) loves (\S+)(,|$)',str, re.I)

print names

if names:
    for group in names:
        print group[0], group[1]

should use find_all()