@ DenverMojo
Commendable efforts on trying to isolate the "problem", which is more than I can say for the deafening silence from Apple so far.
My current situation is now that my wifi connects to my home network only when I'm within 1-2m range from the router.The moment I step out of this range it loses all wifi connectivity - I have tested it by using airplane mode to make sure the phone isn't sneakily using 3G when wifi signal is lost. Actually, my 3G speeds are significantly faster than wifi.
Like others, I have tried all that has been suggested here - reset network settings, reset and forget all settings, restroing ios5, rebooting my router, trying another different new router, assigning static IP addresses, open DNS, disable/enable MAC filtering, assigning DHCP allowed clients, restoring as new phone. Some of these measures work temporarily at best, which serves to ramp up the frustration-o-meter.
I cannot connect to any public wifi networks, tried this at the Apple store in Leicester and they had one look (which took 2 seconds) at my Diagnostics & Usage screen and said "It's a hardware fault, get it replaced". I am awaiting a replacement 4s from Vodafone UK but they are currently out of stock (which is not what they told me last week!), but am not holding out for much with the replacement.
I don't have exactly the same apps as you do. Whilst it could be a possible conflict problem with certain apps, I still suspect it's a fundamental ios5 or hardware fault - or as Apple would call it, a "mathematical problem", much like their antennagate problem when the iPhone 4 was first release. Until Apple refutes this or comes up with a patch/solution, I don't see any reason to not suspect this.
My main gripe is this - why do Apple users put up with this substandard quality/performance everytime?? I absolutely love the 4s for what it tries to be and for what it could be, but I am beginning to wonder if I am just holding onto a romantic notion of an icon that should no longer have this iconic status due to its poor reliability.
As for the conflicting apps / router / interference hypotheses -- if I build a new road, I expect by default for the road to be able to be used by all current road vehicles, especially if I was going charge a toll to drive on my road. Our collective wifi / connectivity / poor battery performance issues suggests substandard planning / troubleshooting and lack of proper real-world testing. Is Apple too big to fail? I think not, is the answer. "It just works" just rings pretty hollow to me at the moment