What Worked –
Uninstalling and Re-installing Kindle App
What Did Not Work –
Closing app and re-opening app
Turning tablet off and then back on again
Settings –> Applications –> Kindle App –> Force Stop
Postscript -> Last night, April 13, 2020, around 11 PM Denver time, Kindle started malfunctioning. It made me re-login repeatedly. Interesting thing though – this post got a number of hits right then. Whatever was going on, it seems to be something from Amazon’s end. It wasn’t just me. It may be that just ignoring it till they fix their problem will take care of things too. At least in some circumstances.