I don't have anything personal to offer as my longest run so far is just over 10 miles. But most of the reason I carry water and fuel with me is that I don't want to break my rhythm, even for a few seconds.

Here's an excerpt from a Chi Running article that was just linked to in this month's newsletter. (Emphasis supplied.)

There are psychological and physiological reasons we recommend working towards running consistently. Psychologically, if you depend on walking breaks for the long term, it can cut you off from discovering your potential, and it does not encourage you to think creatively or resourcefully. Physically, the transition from walking to running and back again can be more taxing than just running. As you learn the ChiRunning technique you'll find that you have a storehouse of tools for dealing with fatigue and pain, should they arise. When you get to the point where you can run 1-3 miles consistently without a break, your first response to pain or fatigue will be to figure out why you're tired or sore, and then try make any necessary corrections or adjustments in your technique. If you need to stop and walk, by all means do so. But there is no reason you should stop to walk if you don't need to. And, the more efficient you become in your running technique, the less tired you'll be. As you learn the ChiRunning technique, you'll see that letting off on your gas pedal and shortening your stride can be even more restful than constantly switching back and forth between walking and running.