As it turns out, I think it’s actually the My Alarm Clock app that was giving it trouble. I’ve tried another alarm clock app and haven’t had the issue yet. When running the original app even without Fully Kiosk running in the background, the app would eventually not respond. Go figure.
Sadly, I really enjoyed that app over the years, but I’m off to fine a new one. You’d be surprised at how few apps there are out there for a bedside tablet clock. Thank you again for your suggestions.