I am in the same boat. I called them and they gave me the same story about being mailed out within a week or two. Specifically, they told me that my permit was approved and waiting to be printed, although their "system is down". I'm not sure exactly what that means. I'm assuming either the printer or logging software was/is broken.
I also learned that Dale Broome is finally gone. Thank goodness, since she never seemed to be able to pick up the phone or respond to emails.
I've also gotten a few of my friends to call their respective representatives to let them know that the Prothonotary's office drags their feet. When I called Gun Owners of America to see if they could light a fire under them, they told me two things:
First, if Delaware had a timeline for approvals (example: 60 days max) then they could sue them for being late. Sadly, that's not the case because Delaware has no such maximum.
Second, if the judges were the ones dragging their feet, they could fund their competitor's reelection campaign to kick the anti-gun judges out. Unfortunately, that can't happen either because the judges are appointed by the governor.
They told me to keep my fingers crossed for a good outcome from the big Supreme Court case starting on November 3rd. Delaware might have to face the music then.