Is there any way to stop the game from putting me in auto-run?

I prefer to hold the shift key to run, and so every time I start the game, I hit Caps Lock to disable auto-run. However, I find it always finds opportunities to re-enable itself. Sometimes I will go through a door that has a loading screen, and I'm auto-running when I come out the other site. Other times I will speak to an NPC and will be running after the conversation has ended.

I tried finding an option in the menu but couldn't. Is there some kind of configuration that would allow me to disable auto-run altogether so that the game doesn't do it for me?

You can change the default autorun state from on to off by editing the game's preference file, which is located in:

My Documents/My games/Skyrim/SkyrimPrefs.ini

In there, you can find the section [Controls] which has a setting

bAlwaysRunByDefault=1

Change it to:

bAlwaysRunByDefault=0

To turn autorun off by default.

The bAlwaysRunByDefault suggestion is useful for when you first start up the game, but the problem isn't what the default is, it's the game toggling your current setting without prompting. This a known issue caused by doing certain things while holding shift. Holding shift while talking to an NPC causes it very consistently. Going through a loading screen does it inconsistently. I've also heard of people experiencing it when getting a killing blow animation.

Edit: Nexus Thread discussing the issue for reference