I've run into this before (and am actually being bit by it now), and my only solution has been to download the file, delete it from the server and re-upload. Far from ideal. If there's an actual solution I'd love to hear it.
I too just got bit by this at a customer as well with a relatively new file running fro a few days the when I went to add another script schedule none were to be found as above. downloading, removing and reposting did nothing. This is really devastating.
Seen this before on a Mac mini. With 12 but never on 13. Also would notice, when looking at the Scheduled Scripts, that the next time shown for a script to run was in the past. Like the admin console/something in the server got stuck. Never tried deleting then re-uploading the file, but a restart of the Mac mini (which hadn't been done/seemed necessary in quite a long time) did the trick. Never figured out the underlying cause, though I always expected it was Java related. Like you said, that shouldn't matter with 13, but perhaps a restart of your machine would be worth a try. I always hate to say "Did you try re-booting it?" but in this case it was the only solution that worked for me.
OK, I fixed the problem, but didn't find the cause.
I was trying to get plugins to activate (another server problem) on my other server, and after I put the plugins (all 3960Works plugins freshly downloaded) in the correct folders, the scripts broke on that server broke with the same symptoms.
So I removed the plugins from both servers, and the script engine is back to working just fine.
So scripts are working, but no server plugins. That will have to be fixed, but for now I can live with this.