Jakob Nielsen’s research has answered this for any application (web apps aren’t special in this regard):
- 0.1 second: Limit for users feeling that they are directly manipulating objects in the UI.
- 1 second: Limit for users feeling that they are freely navigating the command space without having to unduly wait for the computer.
- 10 seconds: Limit for users keeping their attention on the task.
So for web apps you should keep your page response times at 500 ms maximum on average near the servers, to have a web app that is a pleasure to use even with a network latency of 200-300 ms.