What archives are you downloading from that they're overwriting your story if they no longer exist on that site? Can you give a couple of examples? I just checked a story that I know used to be on AO3 but no longer is and it wasn't overwritten. I'm 90% sure the same goes for FFN and TTHFanfic, the main sites I'm currently downloading from.
The Reject List really would only work if you already knew which stories no longer existed on the site so that you could mark them beforehand and you run the risk of accidentally deleting them if you don't uncheck the Delete Books option in the dialogue box. That's not a risk I'd be willing to take.
I think what you want to do is create a custom column for FFDL errors. You can use a text or long text column. Personally, I use a Long Text column called FFDL Errors. Once that's setup go to the Custom Columns tab of Configure Plugin and down the bottom you'll see an option for Special Column: Update/Overwrite Error Column. Tell it which column to update and you're good to go.
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