The common problem that most people have with Sirius' mirror is why Harry never even bothers to check out what he gave him and why Sirius doesn't ask Harry why he isn't using it when Harry talks to him in the fire, but I think the more pressing question is why it's being kept a secret at all?
It was, as far as I can tell, a completely safe and untraceable means of communication, something that everyone should have been happy to provide for Harry, yet Sirius has to sneak it to him during Christmas in complete confidence, warning him not to let Mrs. Weasley see it.
I understand the narrative reasons for not using the mirror, it adds a bit of extra tragedy to the story and if they had had them it would have detracted from the important sense of being isolated and cut off from the world by the Ministry... but on a purely logical level, I see almost no reason why such a safe and secure means of secret communication couldn't have been provided to him from the beginning of the year.
Interesting. Some of the comments below have me thinking that the primary reason it's such a big secret for him and why he doesn't want other Order members to know is that he figures the others would want to control the information he communicates with Harry. Which might also explain why he doesn't ask Harry to use the mirror while talking in the fire, because Lupin was there and might disagree that Harry should have such a thing. It's largely a character flaw. He wants to be in control, otherwise he might have offered the two-way mirrors to be used in other ways.