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Have you tried to connect to another router?
Please take a look at the following FAQ topic:
http://talk.sonymobile.com/t5/FAQ/Wi-Fi-problems/m-p/348104#U348104
I'm having the same issue. Brand new Xperia M conflicting with my laptop's wifi. Any update on solutions?
Xperia M Dual, same problem, installed app Wifi fixer, now it works ok, so it is OS problem.
Thanks for the tip Gyrxiur, unfortunately WiFi Fixer hasn't helped my problem. Are there any settings on the app that I need to change? or should it just sort the problem automatically?