Bluetooth keyboards not connecting properly under iOS 11

Ever since the iOS 11 update, I have had difficulty using my Bluetooth keyboards with my iPad Air. The keyboard connects normally, no error messages or anything. However, if I connect to a Wi-Fi hotspot with a 'pop-up' to sign in or something (like the sort you get at Starbucks), most of the keyboard stops working. (I've learned through trial and error exactly what hotspots cause the problem) If the keyboard in question has a key that functions as the Home button, that button works. But none of the other keys do anything. The iPad can tell the keyboard is connected and acts as if it is, but button presses don't work unless I reboot the iPad. (And the reboot has to be done after I've connected to the Wi-fi and paired the keyboard, it doesn't work otherwise)

I have had this problem with multiple keyboards, both new and old. I've tried forgetting and repairing my Bluetooth devices. I've tried resetting network settings, to no avail. I have done a factory reset and restore, and the problem persists. This problem didn't exist until I updated my iPad to iOS 11.

(If it's relevant, the keyboards in question were an old ThinkOutside Sierra Stowaway, a much newer iClever tri-fold backlit keyboard, and another one that I can't recall the model of because it was a friend's and I was on vacation.)