iPad external display disconnects frequently

I've just gotten an iPad Mini 6th generation (v15.3). I tried using it as an external (AirPlay) display from my MacBook Pro (M1) on Monterey (v12.0.1). I went into display settings and selected the iPad as the extended display and it worked great...for a couple minutes.

After a couple minutes, I could no longer move the cursor onto the display, the display icon in the menu bar disappeared and the only way to get it back was to go back into display settings, disconnect, then reconnect...but then it just happens again.

I've turned off auto-lock on the iPad completely, but that didn't change anything. Am I doing something wrong, or is this just a currently broken feature?