BTT Remote for iOS won't hold connection to BTT for macOS

BTT Remote for iOS (which has always been reliable in the past) won't consistently display available connections. I can make it work for a time, but it'll always stop working again until the settings are manually re-toggled (see below).

I can fix this if I go to BTT's (macOS) System Preferences > BTT Remote > Uncheck then recheck Enable BTT Remote Support. However this only works until the next time the computer goes to sleep or restarts (not sure exactly what makes it lose the connection, but it always does).

Other things tried: Using the BTT Alpha version, uninstalling and reinstalling on iOS and macOS, restarting.

macOS Catalina 10.15.2
iOS 13.3
BTT (macOS) 3.219
BTT Remote (iOS) 2.3.1

Same problem here.

MacOS/iOS: Latest versions.

Same here, and now even manual entry is failing for me.
My instinct is that Big Sur has put something in the way, or rendered BTTRemote incompatible.
(also, now subscribing through Setapp, and wonder if that is complicating matters)

MBP 15, latest OS and iOS

Same problem with current versions MacOSX and iOS...