whsalumni,
The Apple AirPort Extreme Base Station is no longer sold by Apple. The product was pulled from the shelves at the same time that they released the most current update 7.7.7 and 7.6.7 depending upon which version of it you have.
Apple did not release why they pulled this item, it was thought that it was due to the impending FCC deadline for having the 802.11ac standard as approved in place, and the product uses an Apple variant. However they never released the reason for this item pull. It very well could be because of this compatibility issue occurring between the two Apple products that was discovered with the new Wi-Fi chip being used.
If you have another USB-free wireless router available, I would try hooking it up and seeing if it corrects the issue you are having with the iPad Pro. If it does than your warranty for the iPad Pro will cover the AirPort Extreme Base Station too, and I would wait until Apple releases their replacement for the old AirPort Base Station, and then call them and explain how you came upon this issue.
If you don't have another wireless router, you could go to a local Best Buy or Fry's and just get a cheap wireless router that doesn't have a USB port (to be sure you aren't inheriting a NetUSB flaw) and see if the router fixes your issue, you always have 30 days to return it to either store.
Believe it or not, I am merely trying to help in what seemed to me to be an odd issue happening to a small number of people. It's also good to make sure your network is secure and if it has the NetUSB flaw, it is not. I'm not getting anything out of helping here other than the satisfaction of trying to help others, so please don't impugn my integrity.
Best of luck.