I have ben having this problem alot too. I don't know if it was a part of an update, but now when it won't let you do anything because of the pop ups, the game give a message saying you haven't responded in awhile, and if you don't respond soon you will concede.
They need an option to turn off or skip these pop ups.

I had recently encountered this issue as well (no screenshots this time I'm afraid). The opponent was able to produce a stack large enough to time us both out, and I was given a defeat the next turn despite having no action to take (nor initiating the stack to begin with).

I don't know what update had changed this but before all that would happen is the game would result in a draw. Now it can be abused, if an opponent can simply generate a large enough stack they can cheat the win. While ending in a draw was very disappointing, at least there was no incentive to engineer this situation maliciously.

In the short term ending the game in a draw would be preferable. In the long term the game should be able to auto-complete a stack where no further player actions are possible. Programmatically this should be a relatively simple undertaking.

I got the same one: the opponent is creating a lot of creature tokens leading to a timeout. I don't have any problem with it if he's got a timeout for being long but I got the timeout too without any action possible!! Even more: I lost the game because of his timeout