When reconciling my accounts, I have deleted some double entries, twice now. They keep coming back, why is that and how do I delete them permanently?

Sometimes stored cache files within your browser causes QuickBooks not to save changes, warrenmch. 

We can perform a few browser troubleshooting steps and I'd recommend after each steps we'll check if the issue is still showing. 

1. Let's log out and log back in through a private browser. This window doesn't store any history and cache files from visited sites. Then, let's check if the deleted transactions is still showing on the Reconcile page. 
2. We can go back to your main browser to clear or remove the piled-up cache files if you can see that the duplicates are completely deleted and doesn't show up when reconciling. 
3. Other QuickBooks supported browsers can also help us get rid of any unexpected behavior. You can use either Google Chrome, Internet Explorer, and Mozilla Firefox. 

The Audit Log report also provides us the activities made within QuickBooks, like modifying, creating and deleting of transactions. We use it as basis to confirm that the transaction is already deleted. 

Keep me updated on how this works. I'll keep an eye on your reply!