Failing because of a too short timeout feels silly, but a stupidly large timeout leads to frustration and hazardous user actions like killing the app with the task manager.
You don't need a timeout, you need a "cancel" button.
Funny you mention that, this reminds me of Windows task management. Windows automatically gives a popup to terminate an application when it detects an application is unresponsive.
This happens regularly when I open large files in some app, they take a fair bit of time to load, Windows offers a popup to kill the app after few seconds. Have to carefully wait and not click anything.
You don't need a timeout, you need a "cancel" button.