Definitely look in the CJA logs (CJA > Tools > Audit Log). Filter to a date and email that initiated the backfill, once you find the particular component type for a backfill which will be "CONNECTION" in this case, click on the info icon on the right of the description for this particular line and copy the description in the popup. I had a similar issue like this and for some reason it showed as "backFillEnabled": false even though it wasn't which was causing our backfills to fail.
thanks for sharing your experience. I have another case of failed backfill for a dataset, and I'm trying out your technique. I don't have an info icon for the line, which API client are you using?
You can try a few things. In AEP, you can preview the data set there and look at how certain fields are populated. I'd look at whatever you set the person ID to be, in your CJA Connection and ensure you see values populated. And lastly you might have to use the Query Service API, if you can't find the answer from the first approach.