Its nothing to do with routers, it certainly is a problem with Apples software.
I had my iOS 6 (not 6.1) happily working for months with no problems on my Netgear router, then i tried to connect to another Netgear router, i got "incorrect password" i know the password was correct, i even changed it.
My girlfriends new iphone 4s worked fine on the same router, then i go back home, i cannot connect to my own Netgear router, i got to work and cannot connect to my Cisco router.
Then 6.1 update is released, i think maybe that will fix things? I try to update via Itunes, but then keep getting an error when trying to back up lol, "an error has occured" great description Apple. So i cannot perform the update.
In the end i manually backed up my contacts, music, photo's etc etc. Then did factory reset, what a surprise now it all works again. Updated to 6.1 and still works. I can connect to all the routers now.
No firmware upgrades on the routers were performed, as they are all up to date anyway.
Performing the factory reset - wiping it all. This fixed my mine.
Well technically thats what the WIFI standards are for. Apple or anyone else should not be telling anyone how to make WIFI compatible across devices. Thats what the standards are for. If Apple changed something in iOS6 (which apparently they did) it would appear they made some error in the standard. Strangely enough though is, not everyone is having an issue so thats a real head scratcher for sure.
Let me put it in a different way. They are still waiting for Apple to tell them how to make it "compatible" with iOS 6. Of course, if that is indeed "reasonable" demand on router manufacture. I wonder why didn't apple have opening stated that the router is the problem!
Why do some people not have a problem while others do?
Sorry, this is long and will get somewhat technical. : )
[Note: I am not associated with Apple in any way other than a user of their devices]
Connecting to a wi-fi network is not as simple as plugging it in and turning it on.
There are at least 2 hardware devices; each running an operating system of sorts; the access point (router) may run extended software to support specific functions; the wireless device is running software to support the connection; both have extensive configuration settings; both device can be, and usually are, configured by the owner; your iDevice is also running software that you initiate.
In each device there are many layers of hardware and software to establish and maintain your connection. The software in each device shares its resources with everything else that the device is running.
In fact, your iDevice could be running any number of apps, loaded and used, in any sequence. Further, your device may be moving between different access points/routers at different times, and this is all handled automatically and usually invisibly. Maintaining the resources in your iDevice falls to the OS, and in such a small computing device this is a challenge.
The hardware layers are very simple and are built by reputable manufacturers to an international standard. The physical layer is very predictable and usually either works or fails. This "simplicity" is essential if it is to support multiple different devices at once.
The firmware/OS, and the software above that layer, are not as predictable.
If the OS is having difficulty controlling the internal resources, you can see erratic behavior. The fact that I use my iDevice my way, and that is different to, say, my wife, means that we may see different behavior from our iDevices. Unfortunately, this level of flexibility conversely means debugging issues is extremely complex. There are many opportunities within the iDevice for the OS, or the software running on it, to trip up. Just as an example, adding new contact may interact with your wi-fi, adding the contact directly from email introduces another impact, and very quickly the spiderweb grows.
Note that resetting you iDevice, "forgetting" network connections, 'cold starting' the iDevice all give your iDevice the opportunity to clear itself out, in part or full, and start afresh. While this may be inconvenient, it may help you avoid or reduce the symptoms.
In reality, the access point/router is the most stable part of a wireless network. It is not subject to constant updates or change, it does not usually run multiple software in different combinations. The internal resources are not heavily challenged.
* fact - some people have issues while others do not;
* fact - impacts are variable across those who are seeing issues;
* fact - a particular router may be seen as 'working' or 'failing' by different people;
* fact - symptoms become visible at variable time delays;
* fact - symptoms are not easily repeatable;
* fact - there has been some benefit to some people by the interim releases since IOS 6.0;
These are all of significant diagnostic benefit and indicate this issue is very deep.
The fact that Apple is replacing devices indicates that they are taking this seriously.
But...do not expect a quick fix. If that was possible it would be here already. Deep problems need time to explore and resolve. When the issue is found it will more than likely be a compound issue. This will add to the complexity of any resolution.
If you are experiencing problems please activate auto send of diagnostic data (General/About). Apple will use this to try and establish patterns. Without it their job is more difficult ( read: will take longer)
WHAT CAN I DO NOW?
Make sure your router is running the correct firmware. Review the information from the router manufacturer. This is standard procedure and you should check this regularly.
There is nothing you can do about routers/access points that are not in you control.
Replacing your router may provide some symptomatic relief but do not expect it to solve the issues. Netgear is not the boogie-man here. It is conspicuous because it is being vocal and open about its devices and the interaction with IOS. It would be good if other manufacturers could be as open. The bottom line on routers - if you want a new one then buy it. It might improve your situation or it might not. Be clear - it will not fix it. At best it will hide it (but that might be good enough for you).
If you have issues regularly, reboot your iDevice more regularly.
If you cannot join a network you previously have, tell your iDevice to forget that network and cold start the iDevice.
Try and avoid the symptoms as best you can.
Apple are now acknowledging there are issues for some customers and I believe they will fix this, just do not expect it in any defined timeline. In IT terms this really is a piece of string. - how long? ; )