So, what happens at 1 minute is that the AI turns on, and starts sending messages. What you are then seeing is that your game is dying because of the increase in network traffic.
This is caused by either:
1. An outdated network card driver.
2. Outdated router firmware.
3. QoS services on the router that are messing with the stream of AI War data when it spikes higher than the router wants.
4. An unusually low MTU setting on one of the routers, one of the network cards, or one of the ISPs.
There is also a slight possibility this could be a bug in the version of the network library used in the current official version, but I doubt that is what the issue is. If you want to try updating to the latest beta version, though, that does include the ability to lower the game's MTU (thus letting you easily work around #4 if that is the issue), and it includes the latest version of the underlying network library. More info on both is in
this discussion here.
The simplest thing to do is to look at #1 and #2, as those are the most common culprits, even though this isn't that common of an issue overall. At that time I would also look at #3, as that is also a reasonably common culprit and something that can be easily changed on your router.
Hope that helps!