Thanks for sending me your saved game file. I looked at it and didn't find any problems but I think I know what may be causing you confusion.
When you press the checkmark, the weapons popup appears. Just press the checkmark again (with the weapons popup still up) to continue the game. The reason this occurs is that in some situations when you're *manually* firing, you have the option of tapping energy to your weapons (using the round lightning bolt button to the right of the round weapons button) so you can fire again. I admit that in your situation, you don't have any energy weapons to re-energize, but the logic doesn't take this into account.
In order for the game logic to know what you want to do, the popup needs to be up when you continue the game, otherwise, it will direct you to the weapons popup to indicate that you *may* still want to do something.
Anytime you get in a situation where pressing the checkmark button brings up a popup, consider pressing the checkmark button again to ignore further input. One area where this will not work is when asked to pick a new research topic. You'll have to manually choose a topic or select the 'Choose one for me' button to continue the game.
Developer of Starships Unlimited