Hi,
I was having the same problems with MacBook Pro and iMac after upgrading to Lion. I called Apple and what the tech ran me through has now worked for 24 hours with no issues with my Airport Extreme and both my Macs. This includes in and out of sleep, start ups, constant connections, downloads, etc. NOTE: I am running a Windows machine that suffered the same issues so in my case, these seems to clearly be a router issue. This may or may not work on on other routers than the Airport Extreme and only those people using an Apple OS (so you can access the Utility Folder in Applications).
1. Unplug the router
2. While holding the reset button down with a peper clip end plug it back in until the front light is solid orange.
3. When it starts blinking orange, open up Airport Utility in the Utility folder in applications.
4. Completely re-setup your router, choosing WPA2 for security. You can name the router whatever you want.
5. Wait for setup to complete.
6. Link your computer to the new network.
One other thing, if that still doesn't work, Apple told me to look at your avaialble networks to see if there are a lot avaialble. If so, you may be getting some interference from one of the other networks. Apple suggested changing the from Automatic to enter your channel manually, and try random channels until you see fewer or no more other networks other than yours. to do this, go back into Applications>Utilities>Airport Utlity>YOUR ROUTER>Manual Setup. Then navigate to the Wirless tab and switch from Automatic to selecting a different channel. I did this and it seems to have worked for me. Hopefully these steps might work for others.