I have a Nest thermostat and I keep losing connectivity to my airport extreme home network. What would cause this

Incompatible setup.. NEST thermostat are problematic with apple routers..

Redo the setup and set wireless name to short, no spaces and pure alphanumeric.. eg AEwifi

Even fixed wireless channel.. might be a help, try 11, 8, 6. (optional.. some people find it helps others not).

Test with no security.. if that works ok then trial again with WPA2 Personal.. but keep the password 8-20 character pure alphanumeric mixed case and numbers..

Do not hide the network.. MOST IMPORTANT.. networks do not conform to IEEE standard when hiding the name.

Google as there are plenty of posts.. here and in Nest forum

https://community.nest.com/message/20767

Nest thermostat compatible with Airport Extreme

Plenty more https://discussions.apple.com/search?q=nest+thermostat

In addition to the comments from Lapastenague, it might be fair to mention that the Nest is having difficulty with a number of other routers as well. Nest's own Support documents indicate difficulty with a number of popular routers. For example....

Notice that the statement says the routers above may have an issue when using the manufacturer's firmware. Huh? There aren't a lot of other firmware choices out there. In most cases, you have no choice except to use the firmware that the router manufacturer supplies.

The list above probably covers 80-90% of the popular routers that are on the market today.

https://nest.com/support/article/Unsupported-Wi-Fi-Access-Points

Personally, I've tried a Nest Thermostat, and had the same type of difficulties. Every wireless device works just fine, except the Nest....which is located no more than about 10 feet from the wireless router. Nest Support tried hard to help, but the replacement did no better, maybe worse. A third device had difficulty as well. At that point, I returned the product for a refund.

In the light of Bob's experience..

My solution to these sort of problems is to buy a cheap cheap wireless router.. N lite tp-link (not on the list) and run it as WAP.. you can set it up close to the nest and run it on WPA1 not WPA2 with a very short simple password.. but it looks like they are a dog product.

Make sure what you buy is on the dd-wrt list so if things go wrong to you can flash it to something that is usable.

http://www.dd-wrt.com/wiki/index.php/Supported_Devices

Basically, the whole Nest support site consists of disclaimers, which basically say that Nest does not work with the vast majority of wireless routers.

They don't say that TP-Link won't work......so maybe it will.

Have a look at Nest's community forum. As LaPastenague and Bob have mentioned above, Nest has a long history of issues with network communication (going back before Google acquired them). Issues have been reported in connecting to WiFi routers / access points, connectivity to the Nest server (even when the WiFi connection is solid), and battery drain (using power to communicate faster than it can recharge - if you don't have a 'C' wire).

I recommend trying to determine if you are actually losing the WiFi connection or if the WiFi is fine and it is an issue between the thermostat and the Nest server. If you see an Offline status in the app, go into Airport Utility, hold down the option key, and double-click on the device to which the Nest is supposed to connect. See if the Nest shows up in the client list (you need to know the IP and/or MAC address). If it does, then it is more likely an end-to-end (Nest server connectivity) issue. If it repairs itself temporarily after a thermostat restart (or you can just disconnect and reconnect to the WiFi) that is another clue that points to server connectivity.

I spent months taking network traces, identifying issues, and giving all of the info to Nest. Some of the bugs are just dumbfounding, like the thermostat not renewing its DHCP lease when it expires (hence the need for a DHCP reservation). When one of my thermostats crashed on a cold day and it was clear that the same thing could happen when I wasn't home, I realized they weren't ready for prime time and put my tried-and-true basic programmable thermostats back on the walls.

One of the Nest recommendations for users who don't have a C wire is to modify the beacon interval and DTIM settings (wireless stuff) for the SSID on which the thermostat connects. You can't do this on any of the Apple products (default to 100ms and 3 like a lot of other routers). If you have a C wire, that shouldn't matter. I never had any local connectivity issues between the thermostat and an Airport Express.

My experience with Apple Airport Extremes both version 5 and six and Nest thermostats have been very positive. I have two Nest thermostats - one talking to a AE version six at home and a second WE version 5 located at a vacation home - both communication via WIFI without a problem. One unit is the first Nest installed 18 months ago the second in the Nest version 2.

I have not encountered and WIFI connectivity problem. I did have one problem that was attributed to a low battery in the Nest, but that is a feature not a bug. The nest units will disconnect WIFI if the battery drops below a certain voltage.