I still see a random crash here or there with 1.61, however, haven't been able to reproduce and, not happening nearly as often as yours. Steps to try...
Removing any mods that you are using.
Delete the GalCiv3 Folder in your My Documents folder (C:\Users\(Your PC Name)\My Documents\My Games\) Make Sure you back up your old folder. I know this step sucks and takes out all custom factions and ship designs. That's why you back up your original folder so if it's still happening after this step you can restore it.
Assumed you made sure your drivers are up to date.
Completely uninstall game and reinstall it.
Those are my suggestions.