I don't know where you're getting this one month thing.. But when Apple replaces a defective phone, rather the replacement is new or a refurbished model, The warranty carries over from your original device. So if you purchased your original phone that was already replaced less than a year ago then you are still under warranty.. If it's been over a year you're not... I've had Apple swap a phone for me that was a few months passed the warranty so it doesn't hurt to ask.. Just be polite and say that you've Already had the same problem once the replacement only lasted seven months.. They might help you out
This.
Any refurb carries the same warranty as a new iPhone. In fact, most times the refurbs are better as they've gone through more extensive QC.
You shouldn't have to disable various push settings and whatnot - there's no reason you should get the batter life you get above. Take it to Apple and see what they can do.