The same can happen even if the wi-fi signal is strong, if for example, the router needs rebooting (we've been in mom-and-pop coffee shops and actually helped them reboot the router).
To fix these issues, you're forced to disable wi-fi so you can reconnect to the stream via cellular. Annoying, isn't it?
Apple has a "solution." It's something that was found in iOS 6 beta 4 and it is called "Wi-Fi Plus Cellular." The setting is listed in the General->Cellular section.
Assuming the feature isn't removed before iOS 6 ships, it will allow you to tell your iDevices that, even if they are connected to wi-fi, they should automatically switch back to cellular if the wi-fi data flow is sub-optimal.
Sub-optimal is, of course, up to Apple's algorithm to determine. Still, this is a major improvement over current iOS - and Android - versions, which require you, as described above, to manually toggle off wi-fi, then toggle it on again later.
The feature apparently doesn't work for every app, though. Based on the settings options, you can have this feature work on your iCloud Documents, iTunes purchases, Passbook and Reading Lists.
Those with an iPhone or (we assume) cellular capable "new iPad" will be able to also have their FaceTime sessions similarly "protected." The FaceTime option won't appear on any devices earlier than those since FaceTime over cellular is only supported by the iPhone 4S and iPad 3 (and, we assume, the iPhone 5).
[Yes, we know; this means our example above won't be fixed by the feature. It was the most obvious example we could come up with.]
It's a nice new feature. Expect Android to copy it soon, just as Apple copied Android's notification system.