I have added some logic at the bottom of the event sheet
https://dl.dropboxusercontent.com/u/49548363/run_updated.capx
There are some bugs you need to iron out and also you will need to add it into your existing logic as I disabled the movement groups to get it working. From the logic that exists you seem to know what you're doing though so shouldnt be a problem.
Some key things to notice. The RunCounter variable goes to 2 instantly so I set up a 'Can Double Tap' thing. This allows the user to double tap within 1 second. Check the text object to see how it updates with taps. Also you will notice that Run automatically cuts out when the timer expires, you'll need to set up some logic that detects if the player is running when timer ends so it doesn't instantly set back to Stance. Also the Run animation isn't working properly, which I assume is because it's being overriden by something however you had Run working before so this shouldn't be a problem for you. It is definitely triggering Run though! :)
Hopefully this has helped. Any more questions, send them on!
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I disabled my run and movement groups and added those codes.
Here's what happens:
I double tap right arrow (and not release the press on the second tap), player uses Run animation's first frame for about 1 second, then goes back to walk.
so the problems are it never animates the Run and it goes back to walk after a second.