I started having recently this problem and I wonder if there is anything wrong with my setup.
I had in the past many apps of the Amazon Appstore working without any issue.
The only requirement was to keep the Amazon Appstore always installed.
But recently I have some of them not working. When I launch them, I receive a message that the Amazon Appstore is not installed, which is not true.
Any ideas? All permissions and background running are activated.