I was having chronic GI issues that got worse and worse as I went through college. By the fall of my senior year, I was convinced that I had some sort of ulcer that was ravaging my system. It turned out that I was lactose intolerant.
If you can't digest the lactose (a sugar) in milk, it just passes through your system... and the jostling of running to the mix and you will be stopping 25 to 30 minutes into a run.
Here's the rub which might apply to you. You can become lactose intolerant at any point in your life. There apparently is an enzyme in our stomach which we are all born with that lets us digest our mother's milk. Every other animal loses the enzyme, but I guess humans through the domestication of cows and increased milk consumption have managed to sustain it in our systems.
Maybe you have lost the ability to digest milk? You might try going dairy free for a few days and see if that helps. I found that the moment I stopped consuming dairy products, the need to stop on runs went away. Now it is hardly a problem for me. Try it. You don't really need milk products in your diet anyway. The whole "does a body good" thing is marketing hogwash.