I am going to guess this has to do with higher latency and less bandwidth available during this time. Are you able to do/familiar with speed tests. I'd test your connection using a website such as
http://www.speedtest.net/ or dslreports.
I could be mistaken but I'm assuming the latency you're getting during these time periods causes you to time out to the server. I'd test during that time period and during another to see if you get a significant difference.
If you're using windows you can also try going start--->run--->cmd which brings up command prompt
Then try tracert
www.battledawn.com it should show the hops it takes you to get to the server and the latency.
I had a friend once who couldn't navigate the internet at all between the hours of 8pm and 12am due to heavy load on the local internet circuits.
Hopefully this isn't the problem but it sounds as though you may get stuck contacting your ISP. If I don't reply here please send me a PM on the forums as I'd like to help resolve your issue.
~Niracas