From what I can gather from what you are saying, the internet aspect of the router and its IP is not relevant.

You are going Laptop->Wifi->Router->Wifi->N900?

The first thing to do is to plug the laptop directly into the router with a cable, and see if you still get a drop out after 1 minute.

In your router settings under DHCP there will be an option to assign a static IP address for your n900 and laptop. This is what timwatt is referring to. This is worth doing in any case otherwise the IP addresses will change over time and you'll need to keep checking they haven't.