I will play a session of Anno 1404 from the GOG app. Then if I end the session and come back later the play button is not available to click. The only remedy I have found so far is to reboot the PC. Anybody have a solution to this
?

Nobody answered but I figured out what it is doing. But not why. After quitting the game and closing GOG galaxy, If I look in task manager (this is Windows 10), Anno4.exe is still running and also Annoweb4.exe. Also GOG still is running. When I kill those tasks and re-start GOG then play can be started again.
But why were the tasks still running?

I have the same problem. Seems like it doesn't sync properly with GOG Galaxy. Hope GOG fix this problem.

I'm having the same issue. Thanks for the info.

Anno1404 still have to kill tasks to restart the game. Is there a bug forum where it can be reported to GOG ???