You can't for Ally, but you can for escort. As far as I know, these are the fail conditions:
1. Timed mission runs out
2. Boss escapes
3. Escort dies
4. Object you are defending is destroyed (I believe--haven't seen that yet)
For 2, 3, or 4, only fails if it's a required mission objective
My arcs are constantly shifting, just search for GadgetDon for the latest.
The world beware! I've started a blog
GadgetMania Under Attack: The Digg Lockout
I'm having a hard time figuring out when mission failure parameters become available.
Specifically, I want the mission to fail if the ally is defeated, but I don't see the option anywhere.