Some things I'd ask are:
- How exactly does it die? Does it start sputtering then die or does it just turn off?
- Can you restart it immediately? If not, how long until it will start again?
- If it doesn't restart immediately, does it sound like it wants to start but can't, or does the engine just spin?
- If it doesn't restart immediately, is there something you can do to make it start, like maybe with starting fluid, etc?
If you've seen it die after a mile as well as after 100 I'd bet it's not a fuel problem. We had a couple older vehicles that did this exact thing and it was the ignition module. You might get 1 mile or you might get 100, and if you waited a while it would just magically restart as if nothing was wrong. Hot, cold, didn't matter - it was totally random.