Okay, so I'm going to take a shot at answering this. I originally didn't want to as there is actually a lot to say on this topic. But on second thought, I could start with just answering the actual question, and allowing for potential follow-up if additional clarity is needed. So please comment if something isn't clear:
Unlike a Bracha Achrona, which has a time-limit, a Bracha Rishona actually doesn't have a time limit (according to most Poskim).
For example, you can make a Hoadama right now on a bag of chips sitting in front of you, and take as much time as you'd like to munch through the bag. Even pausing for say 1.5 hours in between munches will not clear the effective status of the Bracha Rishona.
However, there are certain things that do affect the Bracha Rishona:
- The additional items must be covered by the original bracha to begin with. There are many rules that govern what items a bracha includes (e.g. same bracha category, in front of you, will be served, having in mind, etc.)
- It can be terminated by a change of location
- It can be terminated by a decision to stop eating (note: the halachic definition of "decision" in this case actually requires a bit more than just a thought)
- It can be terminated by the recital of a Bracha Achrona
- It can be terminated by going to sleep (depends on the type of sleep and various halachic opinions)
- And there are even more...
Keep in mind that each and every one of these bullet points is actually a small representation of a lengthy topic.
So while the bottom line is that time alone will not affect a Bracha Rishona's status (hence the answer to your question: "How long"), many other things can.
The source for most of the above is a careful reading of the seforim: Halachos of Brochos by Rabbi Bodner and The Laws of B'rachos by Rabbi Forst. You may want to read them for additional clarity (they are both written in English).