Some iPhones / iTouchs have experienced No or Intermittent WiFi (wireless ethernet) connectivity.
This issue largely appears after upgrading the firmware to the newest 2.1.1 version.
The theory developed here on Apple's own forums, largely by posters like ScottieWil and Baldwind00 seem to indicate three intertwining issues:
1) The firmware apparently uncaps the WiFi chip, increasing the download speed of the device.
2) The WiFi chip working harder, generates more heat.
3) As LiPo battery ages, the current draw and capacity may fluctuate -aggravated by the WiFi chip drawing more power, and the device heating up more.
4) Further, if the device is squeezed, the back panel may compress tiny metal 'fingers' angled to contact the WiFi chip designed to aid in dissipating heat to a metal panel inside.
Read the Forum for the details.
If the device is in warranty, take/send it to Apple:
If the WiFi is flaky, it may be easier to demonstrate if the battery charge is between 50% and 80% -see the link above or below to the forum....
If the device is out of warranty:
Briefly, one can try to lessen the effects by: (In increasing risk and difficulty)
1) Turn off the auto-brightness. (Saves battery draw.)
2) Turn off Bluetooth when not in use. (Saves battery draw.)
3) Keep the device cool; place on a cool, dry surface. (The device has water indicators inside the headphone and dock openings, water -even from condensation [by placing the device in the freezer -even in a sealed bag] should to be avoided, as this may foul the indicators.)
4) Disassembly is not recommended, however carefully and slightly bending the tiny metal 'fingers' down to better contact the WiFi chip may dissipate heat better.
5) Add a very thin layer of high-quality heat-sync compound to the WiFi chip. (Only if you understand electronics -too thick is as bad as no compound.)
6) Replace the battery. (Provides longer and more stable current.)
Hopefully a solution will be presented, through software to throttle back the WiFi perhaps, or a firmware update.
Thanks to the tireless posters who spent countless hours troubleshooting this issue.
Apple has an amazing user base, and this thread is exceptionally professional and helpful.