Dear God, That sounds almost exactly like my situation with my girlfriend, except that nothing I do seems to turn her on at all, my girlfriends not on the shot, but she's on other meds.
And just to let you know, I fell pretty much the same way that you do.
Now, as for advice, try to get her to try some other type of birth control, unless she has some medical condition that requires she be on a hormonal birth control, because as far as I know, most of the hormone birth control methods kill libido.
If her libido is being killed by the shot, then she is probably not going to see the lack of sex as a problem, because the infrequent, and sometimes absence of sex is still meeting her sexual needs.