My wife and I got new iphones last week. At our rural home in Missouri the wifi works fine, never dropped either of us. Our home in Illinois it drops every time the screen locks. The difference is we have a password on the one that is being dropped, but the one in Missouri is open (no neighbors to steal it). And we have to type in the password every time we connect to it in Illinois, which is very irritating. Why doesn't it remember the ID. But I notice where ever the wifi is unprotected it keeps the connection. The phones are running 4.0.2, by now Apple should be aware of this and they should have had it fixed - this thread is several years old. That's the kind of tech support I have come to know and loathe in MS software.
BTW, our computers never drop the connection while at the same time the iphone does, so it is definately the iphone at fault.