Accessing artifacts after an action re-run

Hey there!
Great job with GitHub Actions! Our team has been using them in anger for a while now.

We have an issue when accessing artifacts.
When we have a failing action, we can see the full artifacts history. However, if we re-run it, we lose these.
This is a bit of a problem for us when we have a flake that gets re-run, and we would like to go back and review the history of the previous run.

Is there any way, given a run ID, we can access its archives?