I dont think you loose connection to your NAT rather your NAT fails or your internet connection just cuts out.
There could be more than one in demigod connections (i dont know too much about this stuff) but only NAT i can think of is in your and other players router (there could even be two on your side if you are realy unlucky), try updating your firmware. Cabel connections (as aposed to ADSL) could be different but but NAT (or NAT rules) is what you configure to portfoward. Unless there is another place it exsits not being able to connect to your NAT is entrirely your fault (i think you are mis dionosing the error).
I would think not being able to connect to a NAT facilitator would simply mean your internet connection/ISP is not working as it should not some complex problem.
Dont think that a NAT acutally physically exsists (its not somthing that you can tenically connect to) its just a bunch of protocols that happend in your router (though there may be a demigod server where there is also a nat).
Edit: you dont need a proxy or 'NAT' connection to connection in demigod do you? (im pretty shure you dont)
Edit 2: you shure its not a DCHP (think thats the accrnum) server (assigns static IPs on your side of the router) dont fail under weekend useage? (this was my problem though it happend a little more often than sporadiacally)