Found this thread searching just now as I started having this problem today. I swapped two routers around in my house to get a better signal in the rooms I'm usually in when home, and while that's been nice for my laptop, it looks like the new router is draining my phone's battery. The problem router is running ddwrt and I'm going to play with some of the settings people have proposed here and see if I can pinpoint anything in particular. For science!
Attached is a screencap just to illustrate the drain and how drastic it can be. A rough timeline so you know what you're looking at: I was mostly home today. The first three-fifths of the graph are idle drain while I was sleeping or home in the morning. Pretty clean data; dips when I used the phone, nice even slope when it was idling. Trace up from the "46s" on the timestamp; at that dip, I installed the router, promptly went out for a bit (drain from using phone while out), and then came back. After that dip, it's still largely idle drain, but the slope speaks for itself.
Premptive edit: Doodled on picture for added clarity.
Postemptive edit: Hmm, competing theory: Where I'm sitting right now, I've got two routers broadcasting a signal. One is good (about -50 rssi), the other varies wildly (from better than the steady one all the way up to the -80 range). I wonder if it's not actually a problem of the phone switching between the two of them when they're both in range. Maybe the first course of action will be to just unplug the further one and see if the supposedly bad router plays nice when it's alone.