Browser Timeouts

It's browser dependent.
"By default, Internet Explorer has a KeepAliveTimeout value of one minute and an additional limiting factor (ServerInfoTimeout) of two minutes. Either setting can cause Internet Explorer to reset the socket." - from IE support http://support.microsoft.com/kb/813827

Firefox is around the same value I think as well.

Usually though server timeout are set lower than browser timeouts, but at least you can control that and set it higher.

You'd rather handle the timeout though, so that way you can act upon such an event.
See this thread: How to detect timeout on an AJAX (XmlHttpRequest) call in the browser?

Increase timeout limit in Google Chrome

Chrome: It is not possible to change the timeout settings in Chrome.
Firefox: You can set the value of network.http.connection-timeout in about:config
IE: It's possible to change the timeout behavior in the windows registry.
Safari: There is a safari extension SafariNoTimeout to extend the timeout from 60s to 10min.

Has Chrome a timeout itself for web service calls?

A webservice call is a regular HTTP call, so it's affected by browser settings regarding http.

I suggest you to look these answers :

General purpose answer :
Where can I find the default timeout settings for all browsers?

Chrome focused answer :
https://superuser.com/questions/633648/how-can-i-change-the-default-website-connection-timeout-in-chrome

Unfortunately, AFAIK there is no setting available in Chrome to set the timeout.

Since last answer of the topic, I don't think Google has improved this but you could at least try the registry approach described there :
Create KeepAliveTimeout and ServerInfoTimeout keys in HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\InternetSettings with desired value in ms and check if it helps.

Additionally, very long http calls are not a very good design. If it's an option, it could be interesting to rework the server process and communication method to have some kind of "keep alive ping" on it, for example to display the progress in client browser instead of freezing it for 10 minutes.

How can I catch a browser timeout and execute my own error message?

Found this awesome workaround using pure javascript, no JScript, no ajax, no external libraries.

Works at treat:

Just need to upload a "test.gif" file to the local site(s).

var url = 'http://192.168.1.89';
var img = new Image();
img.src = url + '/test.gif';
img.onload = function() {
    document.getElementById("msg").innerHTML = "";
    window.location.href = url;
}
img.onerror = function() {
    document.getElementById("msg").innerHTML = "offline";
}

Browser Timeouts