I have that problem with a Samsung S3 also. I've contacted Samsung and they *claim* that they do not have any reported problems with it. If you look on the web, you will see a large number of people with this problem, so I find it extremely difficult to believe that it has never been reported to Samsung. Of course, they say that if I send them the phone, they will look it over and tell me how much it will cost to fix it -- probably more than it would cost to buy a brand new generic Android phone. I've tried it with multiple routers at home and I've even tried it with routers with the security turned completely off. None of my other laptops, tablets, or phones have a problem with my routers and some of the phones are even older than the S3.
This was a phone that I purchased outright at full price, not one of the "free" upgrades that some cellular service providers "give" you for renewing your contract. If they admitted that there was a problem, it would be one thing, but to deny that there is one given the number of reported problems on the internet is completely unacceptable. There is no way I would ever buy another Samsung phone.