I want to edit an import records process in a script. I am not certain I really understand how this works. It seems like the mapping goes away after the first time this script runs and any subsequent time I run it the mapping is lost.

Is mapping permanent in a script? Can I somehow edit this part of my script to verify what is being mapped? Is it possible to do something to cause mapping to be lost?

Once you have the desired import order, set the Import Records step to use Restore and No dialog. Restore is the key to keeping the same order. If you don't select it, the most recently performed import order will be used during subsequent runnings. 'No dialog' will prevent users from modifying the order. When you close the script and have the option to Keep or Replace import order, leave it on the default Keep, unless you want the most recently performed import order to overwrite the original one.

To see what the current order is, run the script (better yet, duplicate the script and delete all other steps) with 'No dialog' deselected.