It appears that Apple broke many people's routers and does not intend to fix it. Wow. I guess this is my last Apple network device.
I tried to update to 7.6.1 twice now with catastrophic results. Let me tell you about the setup. I have a single 4th gen airport extreme, serving wifi to 3 Win7 machines, 4 Macs running Lion, 1 Mac running SL, 3 Apple TVs.
The symptoms are same as many of you. WIFI works fine at first, but after about 24 hours, various devices will start experiencing slowness and unexplained packet drops. The problem worsens over the next few hours until the devices are simply unusable. The problem persists no matter if I reboot the devices or not. The problem IMMEDIATELY goes away for all devices if I reboot the airport extreme. But after another 24 hours, it is back consistently.
I have tried soft and hard reset, manually setting channels, and all the other suggested solutions. I have also upgraded to airport utility 6.0.
I suspect that Apple's testing team is too incompetent to be able to reproduce a slow-onset performance issue like this.
Here's the "solution" that has finally worked for me. First, if you have upgraded to new Airport Utility, download the Airtport Utility 5.6 and install it. Launch it and use the base station menu to downgrade the firmware to 7.5.2. Reboot the Airport Extreme. Problem is gone. Oh, and accept the fact that you may never be able to upgrade your firmware again.