How long can a conversation between a stranger last?

I consider myself an introvert, but am slowly integrating myself into a more sociable person. I've practiced body posture and micro expressions. And although I'm still learning the aforementioned things, I've moved up to conversation techniques such as starting, sustaining, and ending one.

So for now I want to know the longest you've sustained a conversation between a stranger. I will use this information to improve myself, almost like short term goals when I'm out in public.

30 seconds to 2 minutes is probably my best score. I say hi or compliment them, then whether not they say something I sink the conversation into awkwardness.