does the internet connection actually go down or is it just messenger cutting out? - thats the first thing you need to pinpoint.
Your router logs ought to tell you if the connection is actually going down (or atleast you should be able to get an "up time" from the connection in windows). if the internet connection is going down you might want to check your router settings and maybe flash the routers firmware. Also set your network connection to display an icon in your system tray, that way you can see if its connected or not, if the wireless is cutting out it will disappear then reappear a lot - you can check the connection duration (up time) by right clicking and selecting status.
If the connection is staying up then its probably a messenger issue, not sure about what that might be but you might try setting your MTU to 1400