Well, it turns out that Maaya Sakamoto doesn't like mixing her career as a singer with her career as a voice actress, as she pointed out in an interview with director Masaaki Oosumi1:
Sakamoto: [laughter] [...] I'm old-fashioned - I don't want my work as a voice actress to get mixed up with my singing.
—What exactly do you mean by that?
Sakamoto: To me, my job as a singer is not so much a job, as it is a way of expressing myself - which is why I should write my own lyrics and sing under my own name. That's why, as a rule, I don't sing character songs.
Of course, all the OP songs for the Monogatari series are character songs in the usual sense (e.g. Nadeko, rather than Kana Hanazawa, is listed as the singer for "Mousou Express"), and so it makes sense that Maaya Sakamoto wouldn't sing an OP for Shinobu's arc.
Note that there are shows for which Maaya Sakamoto has both sung an OP/ED and voice-acted a character, e.g. RahXephon - but in these cases, it appears that she is credited as herself, rather than as her character. (This is certainly the case for RahXephon's OP "Hemisphere"; I imagine it is also the case for the other anime in which this occurs, but I haven't checked.)
All that said, the Blu-ray version of Second Season does, in fact, have a minute-long opening segment for Shinobu Time. But it's set to the song "white lies", which is not sung by Maaya Sakamoto - it's a non-vocal piece, aside from some choral chanting. (Though I should like to mention that it's an incredible song in its own right, especially if you listen to the full 3'23" version.)
1 To find the bit I've translated here, Ctrl+F for 私も古い考え方.