How strict is the 6-month passport validity rule?

Want to take a trip with wife and kids to Shanghai in November 2014. I am a Russian citizen with US Green Card (rest of the family are US citizens). My passport expires in March 2015. Do I have a chance to get a visa, or is it pointless to even try? I can apply 6 months before the passport expiration, but the trip itself would be within that 6 month window.
If it matters at all- I've previously been to China twice and Hong Kong once.