I can't really say I know what 'stagger or knock' means in this context. 'Stumble' is a common word, but it's usually describing an engine that hesitates or wants to die, usually in response to throttle input.
It sounds to me like you have a misfire. Assumably a mild one (i.e. there is not a cylinder that is entirely worthless), which is why it appears to stop (it doesn't, it's just less noticeable).
That or it's just idling too low.
Check engine light on? Does the car have a tachometer? If so, what's the idle speed, and how much does it vary?