If you lose a potted cutting to mold or rot, should you reuse the soil it was in?

When moss is not in use, how do you store it for the next time?

I do. I pour boiling water on the soil to kill any gnat larvae, let it drain, mix a little of new misture.

is soil so expensive?
anyhow i use rotted soil on established trees.

I reuse it and mix with new stuff as well.

I would use new potting soil. The old soil has microorganisms in it that have killed your cutting(s). I would not deliberately expose newly rooted cuttings to those same pathogenic microbes. I agree with Eli. Well established trees are less problematic.

I never re-use mix from a failed cutting for another cutting. I will use it when transplanting established plants however. 

Personally, I threw out the molded scion trial that I had. But in general, I usually throw old soil into my worm bin after soaking it in the sun for some months in the summer.