Lately I have been noticing Pokémon are running away more frequently if I am moving away from them while trying to capture them. Can anyone confirm that this is true, or is this just a coincidence?
I can only offer anecdotal evidence, but I believe that this is purely coincidental.
I got on the bus, discovered a Pokémon, and threw a ball at it, which hit. 20 minutes later, I realized that the Pokémon had jumped out of the Pokéball, but was still there for me to throw balls at.
This has happened to me twice, and it leads me to believe that the only circumstance in which a Pokémon will escape, is right after a missed throw, or right after escaping a Pokéball.
Once you enter a Pokemon capture sequence, it doesn't matter if you are moving away, moving closer, or stationary. For example, if I was sitting as a passenger in a car, saw a Pokemon, and quickly tapped on it before getting out of range, it would be no different from walking to it and trying to capture it. After going to the screen to capture a Pokemon, you can go out of range, and nothing will happen.
I've noticed this too, but I believe it's just a side effect of Pokemon becoming harder to catch as we level, and also us trying to be more efficient as we play more. I've sometimes caught Pokemon beside a friend that had just started, and they ran away from me after one or two throws and never ran from him. I've also tried stopping as soon as I see a Pokemon and not moving until it's caught, and it still gets away just as often. In short, I'm pretty sure it's due to an increased trainer level which causes them to run away more, not more walking.