Total War: Rome 2
You should, as I wrote, this is very unusual and it has never as far as I am aware been reported either in the Total War reddit or the official forums.
My recommendation: Start a new save game on the Patch 3 Beta, conquer a few territories to increase it (put it on easy if need be for faster testing) and NEVER use the trainer. If it's fixed you have your answer.
I have also noticed that the biggest chunks of Imperium seem to come from completing missions. I'd recommend completing a couple and checking back to see if your Imperium has changed. I'm playing Rome currently, and owning all of Africa gave me a moderate amount of Imperium, but once I completed one of the missions (I think it was conquer 20 factions) I got a sizable boost.
The last thing you should know is that its fine while I'm in game, as this is the first time it started doing this. It goes to not responding I believe just before the AI is done with their moves.
Any help would be appreciated.
firewall and other security software.
on trainer and game.
version and distribution.