What indication do you have that the WiFi was scanning continuously? Where on your task bar is it and what does it look like? The reason is that there is really nothing that would indicate that your Wifi is on and scanning. You'll get a notification that there are networks detected, and when you are connected to WiFi, but if you are getting a "scanning" icon, then it may be something else. There is a GPS icon, that looks like a little sattelite dish that flashes. Is this what you're seeing? That would indicate that some app is trying to acquire your location using GPS or other means.
I haven't noticed any affect on battery from having the wifi searching all the time. Maybe Wifi Analyzer is sucking up your juice. Have you looked at your battery usage (Settings-Applications-Battery Usage) at the times when you think your battery drained fast?