I have had this problem since updating to 1.41. After some number of turns, between 2 and 20, I notice the game does not respond to some actions such as changing production focus, giving actions to ships, building on planets. Ships still seem to move, but it is not possible to end the turn. When I press escape to look at the menu, "Save game", "Load game", and "Main menu" are greyed out, and the mouseover says "Please wait until ship movement, battle, invasion, and colonisation are resolved". This is not in between turns, this is in the middle of my turn, and it doesn't matter how long I wait, the issue never resolves.
The only way to proceed is to retire of exit the game, then load the most recent autosave.
When I use the steam option to "Verify integrity of game cache", it will find that exactly 7 files are not correctly verified and will be redownloaded. This seems to fix the problem for some time, but then after another number of turns, the same issue will resurface. After every time the problem occurs, the steam game cache verification shows the same number of corrupt files.
Any suggestions on how to proceed to fix this bug?