I have many similar crashes, often in v1.3, more in v1.4. The game plays well for a while, but by turn 200, it will crash about once every 5-6 turns, usually at the end of a turn, by turn 300, the crashes come every 2-3 turns, and sometimes in mid-turn, often after completion of a battle, but when other units are still available to move. By turn 450, the game crashes so often that I can't complete even a single turn.
Another surprising thing that happens is when I go into a constricted battlefield (cave, dungeon, certain small cities) with a nine-unit army...the senior commander will not appear. When the battle is over, he has lost all of his hit points and is wounded (his portrait is all red). I stopped fighting with nine-unit armies for the past three weeks, but had the same thing happened today with an 8-unit army.
I am about 50 turns away from completing the new v1.4 scenario, but can't go any farther due to the crashes. I can't even make it halfway through the large Anthys maps.
I am using the lowest resolution possible and a cloth map. I have an AMD Radeon HD 6770M, with the newest driver as of November 7, 2013 running DirectX 11. Only the Steam internet connection is running in the background. The processor is an Intel 7-2600S 2.8 G quad-core unit, with 8GB RAM. This should be able to handle the game easily. It has no problems running Skyrim or the three games in the Bioshock series at high resolution.
When I look at computer memory usage, I can see the game is using a whopping 1,400 MB just prior to crashing.
I have over 250 hours invested in the game, but will do no more until I can play a full campaign. As much as I enjoy the game, it isn't worth the time to invest in a playing a map, only to be unable to finish it after 25 hours of gameplay. I probably had even more hours on Elemental, and it had a lot of similar memory problems, but they were eventually pretty well cleared up. I had even more hours on GalCiv I & II, (all time great games) with no crashes, but they used a lot less memory.