Thanks Teacher 8. from your link,I see why it can't, because it did not record her parents name. However, in old China, there was no such record for poor families. So if her 退休单位 won't do it, what other ways can you suggest?
-You may ask 街道办事处 or 派出所 to issue a (出生)证明 which indicate your mother's name, birth date, birth place and her parents' names and then, go to 公证处 to 公证 this 证明. This is the way most people do.